Single Variable Calculus, Chapter 3, 3.1, Section 3.1, Problem 49

The quantity of oxygen that can dissolve in water depends on the temperature of the water.
The graph below shows how oxygen solubility $S$ varies as a function of the water temperature $T$.



a.) State what is the meaning of the derivative $S'(T)$ and its corresponding units.



b.) Estimate the value of $S'(16)$ and interpret it.






$\quad$ a.) The meaning of the derivative of $S'(T)$ is the rate at which the oxygen solubility changes with respect to the water
temperature; its unit is $\displaystyle \frac{\left(\frac{mg}{L}\right)}{^\circ\rm{C}}$



$\quad$ b.) Based from the graph,


$\qquad \displaystyle S'(16) \approx -0.2 \frac{\frac{mg}{L}}{^\circ\rm{C}}$


$\quad$ This value represents the rate of decrease of the oxygen content of water as the temperature increases.

What does the narrator mean when he says, ''Our departure from Marlow I regard as one of our greatest successes"?

The men stop at the town of Marlow to shop for groceries in Chapter XIII. The narrator describes their venture in the paragraphs that follow this quote. They visit shop after shop and buy something in each one. Instead of being inconvenienced to carry the items themselves, or to have the baskets sent down to their boat, they employ the services of the local shop boys to carry their purchases and to follow along. J. describes the entourage -- which resembles a small parade -- with Montmorency, George and Harris near the front, J. at the rear, and a variety of boys, men, and dogs walking in between. “Our final march down the middle of the High Street, to the river, must have been as imposing a spectacle as Marlow had seen for many a long day,” he says. The scene, and the fact that they could initiate it on their own, serves to validate their mood and assumption of self-importance. And it’s a humorous image for the readers, at the same time. It is a great success, all around.

Can you help me write five short questions from Chapters 1-5 of Hellen Keller's The Story of My Life?

Helen Keller's The Story of My Life is an autobiography in which Keller reflects on her life, especially the time she spent with Anne Sullivan. The first five chapters of the book establish Keller's young childhood illness and her and her parents' journey to help her live as fully as possible while both deaf and blind. The following five questions relate to these chapters:
How old was Helen when she was struck with the fever that would lead to her disabilities?Answer: Nineteen months old
Who first attempted to teach Helen to communicate?Answer: Anne Sullivan
How does Helen react when her rudimentary attempts at communication are misunderstood by her family?Answer: Temper tantrums
Who did the eye doctor refer them to when he could not suggest a surgical option for Helen's vision?Answer: Alexander Graham Bell
What is Helen trying to do when she accidentally sets the house, and herself, on fire?Answer: Dry her apron
http://www.gutenberg.org/ebooks/2397

Here are five questions from the first five chapters of The Story of My Life:
Chapter One: Who was Helen Keller named after? (Answer: She was named after her grandmother, Helen Adams.)
Who were Helen's companions before her teacher, Anne Sullivan, arrived? (Answer: Martha Washington, an African-American girl who was the child of the cook and who understood Helen's signs, and Helen's dog, Belle, were Helen's companions.)
Who was the famous person who referred Helen's parents to the Perkins Institute, the school for the blind in Boston? (Answer: Dr. Alexander Graham Bell referred the family to the Perkins Institute.)
What was the present that Anne Sullivan gave Helen after she arrived at the Kellers' house in Alabama? (Answer: Anne Sullivan gave Helen a doll and then taught her to spell the word "doll.")
By which river did Anne teach Helen? (Answer: Anne brought Helen to the banks of the Tennessee River to learn about nature.)

A uniform electrostatic field points in the +x direction and has a magnitude of E=10 N/C=10 V/m. Find the potential as a function of x, assuming that V=0 at x=0.

Solve for V by knowing that the difference in potential energy is the dot product of the electric field and the infinitesimal path length integrated over the entire path of the particle (from b to a ). Let a be a point in the x=0 plane (where V=0) and let b be and arbitrary positioned point. Once we find the potential at point b we can call this the potential at any point x.
http://www.phys.ufl.edu/~acosta/phy2061/lectures/ElectricPotential.pdf

College Algebra, Chapter 8, Review Exercises, Section Review Exercises, Problem 2

Determine the vertex, focus and directrix of the parabola $\displaystyle x = \frac{1}{12} y^2$ and sketch the graph.

If we rewrite the parabola, we get $y^2 = 12x$. Now, the parabola has the form $y^2 = 4px$ with vertex at $(0,0)$ and opens to the right. The focus is determined to be $(p, 0)$ and the directrix $x = -p$. So if $4p = 12$, then $p = 3$. Thus, the focus lies on $(3,0)$ and the directrix is the line $x = -3$

Does Amir get an internal scar after witnessing the rape of Hassan?

Yes, you could say that Amir is "scarred" by witnessing his friend Hassan being raped. He is certainly traumatized by what he sees and also by his own lack of action: he stands outside the scene but does not intervene to help Hassan. Many readers condemn Amir's actions, but Khaled Hosseini also makes it clear that, despite his abominable actions toward Hassan, Amir also suffers as a result of the assault against Hassan.
After the scene in which Hassan is sexually assaulted in the alley, Amir is both utterly ashamed of himself and desperate to have his sins known. For example, one night when everyone is sleeping, Amir says, "I watched Hassan get raped," to no one (86). Amir says, "A part of me was hoping someone would wake up and hear, so I wouldn't have to live with this lie anymore" (86). Amir feels that it may be worse for no one to ever know what he did (or did not do): "I understood the nature of my new curse: I was going to get away with it" (86). Amir's desire to be punished for the wrong he has committed is also clear in the scene in which he throws pomegranates at Hassan and begs him to throw them back at him. After Amir throws the fruit at Hassan, he exclaims, "Get up! Hit me! . . . Hit me back! Hit me back, goddamn you!" (92). Hassan does not fulfill Amir's request and instead hits himself in the face with a pomegranate. We can also see Amir projecting his own guilt onto Hassan by calling him a coward in this scene. These examples suggest that Amir feels immense regret for what he has done and can only move past the incident if he faces appropriate consequences.
Amir, though, avoids Hassan and then manages to get him and Ali to leave Baba's house before Baba and Amir move to America—never to see their servants/friends again. As an adult, some twenty years later, Amir is still haunted by his actions and inaction; this is why he is so struck when Rahim Khan calls him and tells him, "There is a way to be good again" (2). Amir embarks on a redemptive quest that sees him overcome numerous obstacles to rescue and adopt Sohrab, Hassan's son. One of the most significant scenes involves Amir physically fighting Assef, Hassan's assailant and Sohrab's abuser, until Amir is nearly killed. In this fight, Amir acquires a symbolic physical scar. Amir recalls, "I kept thinking of something else Dr. Faruqi had said: "The impact had cut your upper lip in two . . . clean down the middle. Clean down the middle. Like a harelip" (297). This is significant because Hassan was born with a harelip, which Baba had a surgeon fix for Hassan's birthday one year. Amir now feels to some extent like Hassan, since he has been physically beaten by Assef and also carries a scar that will always remind him of Hassan. The fight also provides Amir with a sense of relief; he feels cleansed because he is finally being physically punished. Amir laughs while Assef punches him and explains, "My body was broken . . . but I felt healed. Healed at last. I laughed" (289). It seems symbolically appropriate, too, that Amir now has a physical scar to match his inner pain, and this scar also seems to help him externalize his guilt and venture beyond (or begin to) the sins of his childhood.

Summarize the Importance of funding mental health regarding mentally ill individuals in prison

Much has been written on the importance of taking care of prisoners' mental health, both while they are in the system and upon their release. Recidivism rates are greatly increased where prisoners are unsupported after they have been released from prison, with one contributing factor being that prisoners' mental health issues often go untreated.
Mental health funding is lacking in the general population, as well as the prison population, and taxpayers can often be loath to see their tax dollars being spent on the incarcerated. In the long run, however, studies show it benefits society to ensure that the mental health needs of offenders are met. In the UK, it was identified that suicide rates in prison have risen shortly over the past decade, and over 70% of suicides in prison are committed by inmates found to have mental health issues. This is an issue because prisoners' needs are also important. From a community perspective, however, perhaps the more pressing concern is the disproportionate number of mentally ill individuals who are both existent within the prison system and released, untreated, into the general population every year.
Studies have shown that close to 20% of those imprisoned in the United States have some form of mental health issue, far higher than that in the general population. There is, in many cases, a direct correlation between mental health issues and the commission of crimes. Numerous individuals are driven to crime by their untreated mental health needs. Where these individuals enter and then leave the prison population without having these needs addressed, the likelihood that they will once again be driven to crime by mental illness is high. The connection between violent crime and serious mental illness has been demonstrated again and again.
Often, "mental health issues" is interpreted to mean illnesses like schizophrenia and borderline personality disorder, which certainly can contribute to offending. However, the vast majority of mental health issues identified in prison are connected to drug and alcohol addiction, with a significant proportion of crimes being committed by those under the influence of these substances. As such, it is to the benefit of society to spend money on funding programs to help prisoners addicted to these substances. Where prisoners can be released from prison clean of their addictions, and can be offered ongoing support outside of the prison environment to remain clean, it is far less likely that they will relapse and commit further crimes under the influence of toxic substances. Put shortly, ongoing mental health support for ex-prisoners slashes recidivism rates.
It can be difficult to summon public support for any program involving offenders, or indeed involving mental illness. However, in this group, the connections between the two issues are starkly drawn and it is demonstrably to the benefit of society as a whole to ensure that the mental illnesses of prisoners, which correlate directly with an increased tendency to offend and reoffend, are dealt with both in prison and upon reintegration into society.
https://www.nao.org.uk/report/mental-health-in-prisons/

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3793843/

Why isn’t Jess wearing a shirt or shorts?

Jess goes running in overalls because he thinks he'll be too hot if he wears clothes underneath them.
Jess gets up early every morning in the summer to go running; he's up early enough that he worries his mother will get mad if he wakes her. He wants to improve his speed so that by the time school starts, he's the best runner in the fifth grade.
When he wakes, he puts on his overalls right away. He doesn't bother with a shirt. Paterson writes:

He didn't worry about a shirt because once he began running he would be hot as popping grease even if the morning air was chill, or shoes because the bottoms of his feet were by now as tough as his worn-out sneakers.

The exertion of running will heat up his body so that he won't feel the cold air on it. When he leaves the house, Jess notices that he can see his breath in the air even though it's August. He thinks, too, that by the time he's doing chores in the afternoon it will be plenty hot. By the time he gets home, he's aching and sweaty.

Discuss the relationship between the ideology of the American Revolution and the emergence of anti-slavery thinking in the United States and Great Britain.

Both the ideology of the American Revolution and that of abolitionism are grounded in Enlightenment thinking. One of the key notions in Enlightenment political thought was thinking about the nature of human rights. Rather than seeing society as a natural hierarchy with God at the pinnacle, then angels next, then human rulers and aristocrats, then ordinary people, and then animals, plants, and minerals, with those at the top of the hierarchy being naturally better than those at the bottom and thus having more power, the Enlightenment thinkers began with the individual human and saw human associations and hierarchies as something that evolved historically rather than being grounded in a divinely authorized hierarchy.
The Declaration of Independence reflects this form of Enlightenment thought in the first sentence of its second paragraph:

We hold these truths to be self-evident, that all men are created equal, that they are endowed . . . with certain unalienable Rights, that among these are Life, Liberty, and the pursuit of Happiness.

This notion of all people being created equal is the basis of abolitionism. Rather than viewing people as part of a natural hierarchy, something that might justify some being owners and some being slaves, both the founders of the United States and the abolitionists held that all people were created equal. Thus, government is only legitimate insofar as it operates with the consent of the governed. Since slaves do not consent to their slavery but instead have it imposed on them, it is illegitimate according to the Lockean account of government underpinning the Declaration of Independence.

Calculus: Early Transcendentals, Chapter 4, 4.4, Section 4.4, Problem 51

lim_(x->0^+) (1/x-1/(e^x-1))
Plug-in x=0 to the function.
lim_(x->0^+) (1/x-1/(e^x-1)) = 1/0-1/(e^0-1)=oo - oo
Since the result is indeterminate, to take its limit apply L'Hospital's Rule. To do so, expression the function as one fraction.
lim_(x->0^+) (1/x-1/(e^x-1)) = lim_(x->0^+) ((e^x-1)/(x(e^x-1)) - x/(x(e^x-1)))=lim_(x->0^+) (e^x-x-1)/(x(e^x-1))
Then, take the derivative of the numerator and denominator.
lim_(x->0^+) ((e^x-x-1)')/((x(e^x-1))')=lim_(x->0^+) (e^x-1-0)/(x*e^x + 1*(e^x-1)) = lim_(x->0^+) (e^x-1)/(xe^x + e^x-1)
And, plug-in x=0.
lim_(x->0^+)(e^x-1)/(xe^x+e^x-1)= (e^0-1)/(0*e^0+e^0-1) = 0/0
Since the result it still indeterminate, apply L'Hospitals Rule again. Take the derivative of the numerator and denominator.
lim_(x->0^+) ((e^x-1)')/((xe^x+e^x-1)') = lim_(x->0^+) (e^x-0)/(x*e^x+1*e^x+e^x-0) = lim_(x->0^+) e^x/(xe^x + 2e^x) = lim_(x->0^+)1/(x+2)
And, plug-in x=0.
lim_(x->0^+)(1/x+2)=1/(0+2)=1/2

Therefore, lim_(x->0^+) (1/x -1/(e^x-1)) = 1/2 .

Calculus of a Single Variable, Chapter 5, 5.2, Section 5.2, Problem 14

int(x^2+4x)/(x^3+6x^2+5)dx=
We will use the following formula: int(f'(x))/(f(x))dx=ln|f(x)|+C
The formula tells us that if we have integral of rational function where the numerator is equal to the derivative of the denominator, then the integral is equal to natural logarithm of the denominator plus some constant. The proof of the formula can be obtained by simply integrating the right-hand side.
Since (x^3+6x^2+5)'=3x^2+12x=3(x^2+4x) we must first modify the integral in order to apply the formula. We will both multiply and divide the integral by 3.
1/3int(3x^2+12x)/(x^3+6x^2+5)dx=
Now we apply the formula to obtain the final result.
1/3ln|x^3+6x^2+5|+C

Why does Mama insist Liesel pick up and deliver the washing?

Rosa's just lost a valuable customer and doesn't want to lose any more if she can help it. As always, she takes out her frustration on Liesel, giving her more laundry to do as well as subjecting her to a characteristically brutal tongue-lashing. For good measure, Rosa tells Liesel that, from now on, she'll be the one to venture out to pick up and deliver laundry. And when she does so, she's under strict instructions from Rosa to put on a sad face and tell her customers, especially the rich ones, that Rosa's sick.
It's hoped that eliciting sympathy in such a shameless manner will make it less likely that customers will cancel their orders. Liesel obeys without question; but then, she has no choice. Rosa's threatened her with a good, hard smack with the wooden spoon if she doesn't do as she's told.

In Markus Zusak's The Book Thief, Liesel Meminger is a young girl living in Germany during the time of the Nazi regime in World War II. The book is narrated by Death itself, who sees Liesel's younger brother die near the very beginning of the book.
Her father has been taken away because he is a suspected communist, and Liesel's mother could be taken away as well because she is connected to her possibly communist husband, so Liesel is taken in by Hans and Rosa Hubermann, who act as foster parents. Rosa, or Mama, works doing laundry for the people in their town. Rosa is a pretty harsh person, and Nazi Germany is becoming a harder and harder place to live in, including in terms of the economy. She hopes that by having Liesel, a child, pick up and deliver laundry, people will have sympathy for her and keep using Rosa's laundry service.

Which surface wave vibrates at right angles to its direction of motion? p-wave s-wave Love wave Rayleigh wave

This question requires us to understand each of these four types of seismic wave. Once we know how each one works, we can see which one best fits the description of a surface wave that vibrates at right angles.P-waves propagate longitudinally; that is, the vibration is along a line parallel to the direction in which the wave propagates. So that can't be the answer.
S-waves propagate transversely; that is, at right angles to the direction of motion. However, they are body waves that propagate across the entire body of rock, not surface waves as the question asked. So that can't be the answer either.Love waves also propagate transversely, and furthermore they are surface waves; so this is most likely the answer. But let's see about the fourth option, just in case.
Rayleigh waves propagate both transversely and longitudinally, and they are surface waves as well. So while this could be an answer, it's not the best answer because love waves are only transverse while Rayleigh waves are both transverse and longitudinal.

Single Variable Calculus, Chapter 3, 3.9, Section 3.9, Problem 38

Prove that the relative change in $F$ is about 4 times the relative change in $R$. State how will a 5% increase in the radius affect the flow of blood.
Taking the derivative of $F$ with respect to $R$, we have

$
\begin{equation}
\begin{aligned}
\frac{dF}{dR} &= K \frac{d}{dR} (R^4)\\
\\
\frac{dF}{dR} &= K (4R^3)\\
\\
\frac{dF}{dR} &= 4KR^2\\
\\
dF &= 4KR^3 \quad \text{or} \quad \Delta F = 4KR^3 \Delta R

\end{aligned}
\end{equation}
$


Hence, the relative error is,
$\displaystyle \frac{\Delta F}{F} = \frac{\Delta \cancel{K}R^3\Delta R}{\cancel{K}R^4} = 4 \frac{\Delta R}{R}$
When the increase in radius is 5%

$
\begin{equation}
\begin{aligned}
\frac{\Delta F}{F} &= 4 (5 \%)\\
\\
\frac{\Delta F}{F} &= 20 \%
\end{aligned}
\end{equation}
$


The flow of blood is increased yb 20%

What's wrong with the first planet in chapter 5?

When Meg arrives on the first planet, she feels an enormous sense of pressure, as if she is being flattened by a steamroller. She can't breathe, because she can't get her lungs to rise and fall. To her, this feels very different from not having enough oxygen. Her mind also feels flattened out, making it difficult to think, and she finds her heart can't beat properly.
All of this occurs because the first planet is two-dimensional, not three-dimensional.
Mrs. Which has taken them there by mistake. Not corporeal herself, though she takes on a human guise, she forgets that the children can't survive on a two-dimensional planet. She simply remembers it as a pleasant place that she, Mrs. Whatsit, and Mrs. Who enjoy visiting.

How would you analyse the poem "Evening in Paradise" by John Milton? What literary devices appear in it?

"Evening in Paradise" is from the epic poem Paradise Lost written by John Milton.
In summary, the poem describes the approach of evening and the animals settling in for the night—except for the Nightingale that will sing all night long. Then stars appear in the sky and are then joined by the moon: they illuminate the darkness with light.
In the first two lines, the reader recognizes the imagery used in the form of personification.
Personification is:

...a figure of speech in which abstractions, animals, ideas, and inanimate objects are endowed with human form, character, traits, or sensibilities

"Evening" is referred to with the possessive pronoun "her," and the poet describes that she has "clad" (clothed) all things in the color of "Twilight gray." The idea of clothing something—and being clothed—is a human behavior, and the "Evening" is not human, but given human characteristics.

Now came still Evening on, and Twilight gray Had in her sober Liverie all things clad... (1-2)

Lines five and six describe the singing of the "Nightingale." Imagery is used as the author describes her song as an "amorous descant," or a love song. (A "descant" is a "song or a melody.")

...all but the wakeful Nightingale; She all night long her amorous descant sung... (5-6)

In line seven, "Silence" is personified. Silence is not a person, therefore it cannot experience emotions, such as (in this case) pleasure.

Silence was pleas'd... (7)

Note that in line seven, Milton refers to the "Firmament," which is "the vault of heaven; [the] sky." A metaphor is used once again: this time the two things being compared are the stars and "Saphirs" (sapphires). Both are shiny and bright (the characteristics they share), but one is a heavenly body of gases and the other is a gem.

Now glow'd the Firmament With living Saphirs... (7-8)

In lines nine and ten, the author alludes to Hesperus. In Greek mythology, it was believed that Hesperus was the evening star or the planet Venus. In the poem, Hesperus ushers in the "starrie Host" (the stars)—he himself shining the brightest.

Hesperus that led The starrie Host, rode brightest... (8-9)

Hesperus is the brightest of them all, but only until the moon appears. Once again, personification is used to describe "the Moon." The possessive pronoun is used ("her"), and she is described as uncovering ("unvail'd") her unequaled ("peerless") light—in doing so, the moon throws over the darkness a silver light ("her Silver Mantle threw"). The use of "mantle" is also an example of personification, in that a mantle (cloak or cape) is an article of clothing that people wear.

...till the Moon Rising in clouded Majestie, at length Apparent Queen unvail'd her peerless light, And o're the dark her Silver Mantle threw. (9-12)

Milton's uses of imagery provide vivid descriptions that bring his subject matter alive.

Why don't Harrison's parents respond with more feelings to what they have seen ?

In the dystopian society depicted in such horrifying detail by Vonnegut, people aren't supposed to feel anything. They're simply supposed to do what the government tells them. For its citizens to enjoy a rich emotional life is dangerous to the government, as it provides a haven of repose, a personal space where people can escape the state's control. Handicaps must then be used to enforce not only a crude physical and intellectual equality but also an emotional one. So when the Bergerons watch their son's death on live TV, they've been so emotionally crippled that they're unable to feel sad for more than a few brief moments. Hazel is not a particularly bright individual, so she's naturally handicapped and inured to any deep emotions. George is naturally intelligent, however, and so he is forced to wear a radio device that emits loud noise at regular intervals to prevent him from experiencing sustained thought or emotion.

Harrison's parents do not respond to what they see on the television screen because Hazel is rather dull and George must wear a handicap on his head that prevents his thoughts from forming.
Whenever George has a thought that is the least bit complicated a buzzer goes off in his head, destroying his ideas and injecting pain. Hazel is naturally "normal," so she is not intelligent and sensitive enough to experience anything but the simplest feelings. When they see their son Harrison on the television screen after having heard that he has escaped from jail, they do not react in the expected manner of parents because George has a terrible ringing from his handicaps, This ringing in his ears prevents George's thoughts from forming as they normally would, while Mable is simply not capable of feeling anything of any depth.

What are the roles of Dr. B. R. Ambedkar, Sarojini Naidu, and Rajendra Prasad in Indian society?

B. R. Ambedkar, Sarojini Naidu, and Rajendra Prasad played a vital role in Indian society because of their contributions to Indian independence.
B.R. Ambedkar's role in Indian society can be felt today as he was an important voice in crafting India's constitution. B.R. Ambedekar was vocal in suggesting that a free India had to embrace equality in as many forms as possible. He was a fierce opponent of "untouchability," the idea that society should be stratified into higher and lower castes. He argued that an independent India should be free of caste discrimination, going as far as embedding this idea in the new nation's constitution.
Sarojini Naidu was called "the nightingale of India."   Her writing and public oration reflected her passion towards Indian freedom from British control. Naidu used her renown as an artist to become a force of political change. She was active in the Indian National Congress movement. In the 1940s, she participated in the "Quit India" movement.  Despite being jailed, she did not reject her insistence on a free and independent India.  When India achieved Independence in 1947, "the nightingale" became a part of political history as she became governor of the state of Uttar Pradesh.  She was the first woman to serve in such a capacity.
Rajendra Prasad was the first president of India.  Prasad was an important force in the movement for Indian independence.  He worked with Mahatma Gandhi as an agent of non-violent civil disobedience and took part in Gandhi's Salt March.  Like Gandhi, he was imprisoned for his political actions. However, with independence, he became India's first president. 
Indian society views Ambedkar, Naidu, and Prasad as important forces. Indian independence is due, in large part, to their contributions.  Even after achieving freedom, their commitment to the country was underscored by their public service to the fledgling republic.  In Ambedkar's insistence on banishing caste discrimination, the promises and possibilities of the world's largest democracy can be realized.  Naidu's example proved that the new nation could welcome women and men as political brokers of power. Finally, President Prasad demonstrated how civic duty is the ultimate reflection of love of country.  Each of them saw a vision for the new India, a reality that Indian society appreciates and still pursues today.

solve f(4/5)=Integral(0 to 1) e^-2x dx

Hello!
Unfortunately, your question contains an unknown function f, and it is present only at the left part of the equation with the value 4/5 as an argument. We can find this number f(4/5), but not the function f itself.
With this in mind, compute the integral from the right part:
int_0^1 e^(-2x) dx = |t = - 2 x, t\in [0, -2], x = - 1 / 2 t, dx = - 1 / 2 dt| =

= int_0^(-2) e^t (- 1 / 2) dt = 1 / 2 int_(-2)^0 e^t dt = 1 / 2 e^t|_(t = -2)^0 = 1 / 2(e^0 - e^(-2)) = 1/2(1 - 1/e^2) approx -0.432.
We used a simple substitution t=-2x and the fact that int_a^b g(t) dt = -int_b^a g(t) dt.
So we know that f(4/5) =1/2(1-1/e^2) but know nothing more about the function f.
Please tell me if there was some error in the conditions, and I will update the solution.

In "The Road Not Taken," why did the traveler find it difficult to make his choice on that particular morning? What impression do you form of the traveler?

In Robert Frost’s poem “The Road Not Taken,” the traveler is making of choice of which path to take as he hikes through the woods. This becomes a modern metaphor for his life. As the traveler approaches a fork in the road he stops to examine both for use. On that particular morning, the roads seem very similar, but one seemed to be a bit less worn, thereforehe decided to take that one while keeping the other one for another day. He knows he will never travel that way again, yet he is introspective saying, “I took the one less traveled by, And that has made all the difference.”
There are contradictions in the words as Frost tells the audience the two paths were quite the same, with the second one having a bit less wear on that particular morning. Later the traveler explains he took the one less traveled by and that made all the difference.
Since poetry is meant to be interpreted and appreciated, this one is generally associated the pursuit of individualism and adventure. Readers say the traveler was daring as he chose to take the path that “wanted wear” and feel this affected his life for years to come. Others feel Robert Frost was writing about his indecisive friend and the poem was never meant to carry its modern connotation of encouraging people to be adventurous and to follow their dreams. In either case, the traveler has to make a decision, which he looks back on pensively at the end of the poem.

What conflict does Mehetabel need to overcome in "The Bedquilt"?

The conflict exhibited in Fisher's short story is self versus society. Thus, Mehetabel needs to reconcile how society values a woman of her age and how she should value herself.
In the story, Mehetabel is sixty-eight years old, living during a time in New England in which "an unmarried woman was an old maid at twenty" and by "forty was everyone's servant." Because of Mehetabel's advanced years and her spinster status, she is treated as an extraneous member of her family and society. 
Everyone in Mehetabel's household thinks of her as a servant, and she is given the worst chores to perform. Mehetabel has little choice but to accept her family's indifference toward her. In her era, an elderly spinster's position in society was a tenuous one, dependent upon the goodwill of all. 
However, there is one thing that distinguishes Mehetabel from the rest of the family: she is a genius at patchwork. It is this ability that finally elevates her in the eyes of her family and her community. The story ends with Mehetabel finally receiving the recognition she deserves, after winning a blue ribbon at the county fair for her work.
Mehetabel comes to realize that she is a valuable member of her society and that her sense of worth need not be determined by arbitrary societal norms.

Please select events relating to the NYPD (New York City Police Department) in the past that are still important today and explain why you chose those events.

There are many past events that continue to affect the New York City Police Department (NYPD). Perhaps one of the most important is the NYPD's involvement in the September 11, 2001, terrorist attacks on the World Trade Center. In the events surrounding those attacks, the NYPD lost 23 officers and that year was the deadliest in the NYPD's history. As a result, the NYPD created the Counter-Terrorism Bureau in 2002. 
Many people would also say that the death of Eric Garner, an African-American man in Staten Island, in 2014, still affects community-police relations in New York City today. Garner was placed in a police chokehold and died, and an investigation revealed that he died as a result of the chokehold and ill health. The NYPD does not allow officers to place people in chokeholds. As a result of his death (in the context of the deaths of many African Americans across the country at the hands of the police), there were many public protests. While the officer who held Garner was not indicted, the Department of Justice opened an investigation into Garner's death. Many people regard Garner's death as symbolic of police brutality, particularly against people of color, in New York City. Perhaps there are other events in the history of the NYPD that you think still have an effect on the organization.  

Why is Clarisse's uncle arrested in Fahrenheit 451 by Ray Bradbury?

During Montag's first conversation with Clarisse, Montag asks her what is going on in her home that the lights have to be turned on. Clarisse responds by telling Montag that her mother, father, and uncle are sitting together having a conversation, which is considered odd behavior in Bradbury's dystopian society. Clarisse then explains to Montag that her uncle was arrested before for being a pedestrian. In Bradbury's dystopian society, intellectual pursuits are discouraged, and novels are considered illegal. Anyone possessing or distributing literature is arrested, and their books are destroyed by fire. Being a pedestrian is synonymous with appreciating nature, science, independence, and thinking deeply. These activities are virtually unheard of in Bradbury's dystopian society, where citizens are typically watching their parlour walls or participating in violent games. The government fears intellectuals and does not want to compete with critics, which is why being a pedestrian is suspicious and can lead to a citizen's arrest.

Clarisse's uncle is arrested for driving too slowly on the highway. He was once caught driving at forty miles an hour; as a result, he was jailed for two days.
Clarisse tells Montag no one really notices the details in life, as no one is allowed to slow down long enough to observe anything. Basically, Clarisse and Montag live in a totalitarian world, where citizens aren't allowed individual, autonomous thoughts that aren't sanctioned by the government. To keep its citizens docile and subservient, the government creates draconian and arbitrary laws that permeate every aspect of life. Failure to comply is met with stringent punishment.
Clarisse maintains that people have to drive so fast that they can't make out what they're seeing. They must imagine a green blur stands in for grass, a pink blur stands in for a rose-garden, a white blur stands in for a house, and a brown blur designates a cow.

What are the basic differences in the attitudes of Lord Canterville and Mr. Otis?

The most basic attitude difference between Mr. Otis and Lord Canterville is their attitude toward the ghost.  
The attitude difference starts out as a difference in belief.  Lord Canterville believes that the ghost is real.  Mr. Otis does not believe the ghost of Sir Simon is real.  He even states that if ghosts were a real thing, then the Americans would already have one on display in a museum.  

"I have come from a modern country, where we have everything that money can buy; and with all our spry young fellows painting the Old World red, and carrying off your best actors and primadonnas, I reckon that if there were such a thing as a ghost in Europe, we'd have it at home in a very short time in one of our public museums, or on the road as a show."

Eventually, Mr. Otis comes to accept the fact that the ghost is real.  This leads to the second attitude difference between Lord Canterville and Mr. Otis.  Lord Canterville accepts the ghost's presence as an unfortunate consequence of the property.  He believes that nothing can be done about the ghost.  Mr. Otis, on the other hand, believes that the ghost problem can be solved.  Mr. Otis, and most of his family, view the ghost as a mild inconvenience of the home -- an inconvenience that can be fixed.  

"Upon the other hand," he continued, "if he really declines to use the Rising Sun Lubricator, we shall have to take his chains from him. It would be quite impossible to sleep, with such a noise going on outside the bedrooms."

 
 

Calculus of a Single Variable, Chapter 8, 8.1, Section 8.1, Problem 34

To evaluate the given integral problem: int 2/(7e^x+4)dx , we may apply u-substitution using: u= e^x then du = e^x dx .
Plug-in u = e^x on du= e^x dx , we get: du = u dx or (du)/u =dx
The integral becomes:
int 2/(7e^x+4)dx =int 2/(7u+4)* (du)/u
=int 2/(7u^2+4u)du
Apply the basic properties of integration: int c*f(x) dx= c int f(x) dx .
int 2/(7u^2+4u)du =2int 1/(7u^2+4u)du
Apply completing the square: 7u^2+4u =(sqrt(7)u+2/sqrt(7))^2 -4/7
2int 1/(7u^2+4u)du =2int 1/((sqrt(7)u+2/sqrt(7))^2 -4/7)du


Let v =sqrt(7)u+2/sqrt(7) then dv = sqrt(7) du or (dv)/sqrt(7) = du .
The integral becomes:
2int 1/(7u^2+4u)du =2 int 1/(v^2 -4/7) *(dv)/sqrt(7)
Rationalize the denominator:
2 int 1/(v^2 -4/7) *(dv)/sqrt(7) *sqrt(7)/sqrt(7)
= 2 int (sqrt(7)dv)/ ( 7*(v^2 -4/7))
=2 int (sqrt(7)dv)/ ( 7v^2 -4)

From the table of integrals, we may apply int dx/(x^2-a^2) = 1/(2a)ln[(u-a)/(u+a)]+C
Let: w = sqrt(7)v then dw = sqrt(7) dv
2int (sqrt(7) dv)/ ( 7v^2 -4) =2int (sqrt(7) dv)/ (( sqrt(7)v)^2 -2^2)
= 2 int (dw)/ (w^2-2^2)
= 2 *1/(2*2)ln[(w-2)/(w+2)]+C
=1/2ln[(w-2)/(w+2)]+C
Recall we let: w =sqrt(7)v and v =sqrt(7)u+2/sqrt(7) .
Then, w=sqrt(7)*[sqrt(7)u+2/sqrt(7)] = 7u +2
Plug-in u =e^x on w=7u +2 , we get: w= 7e^x+2
The indefinite integral will be:
int 2/(7e^x+4)dx =1/2ln[(7e^x+2-2)/(7e^x+2+2)]+C
=1/2ln[(7e^x)/(7e^x+4)]+C

int (x+1) / sqrt(3x^2+6x) dx Find the indefinite integral

int (x + 1)/sqrt(3x^2+6x) dx
To solve, apply u-substitution method.

u = 3x^2+6x
du = (6x+6)dx
du = 6(x + 1)dx
1/6du = (x +1)dx

Expressing the integral in terms of u, it becomes
= int 1/sqrt(3x^2 + 6x)*(x + 1)dx
= int 1/sqrtu *1/6 du
= 1/6 int1/sqrtu du
Then, convert the radical to exponent form.
= 1/6 int 1/u^(1/2)du
Also, apply the negative exponent rule a^(-m) = 1/a^m .
= 1/6 int u^(-1/2) du
To take the integral of this, apply the formula int x^n dx = x^(n+1)/(n+1)+C .
= 1/6 *u^(1/2)/(1/2) + C
= 1/6 * (2u^(1/2))/1+C
=u^(1/2)/3+C
= sqrtu /3 + C
And, substitute back u = 3x^2+6x .
= sqrt(3x^2+6x) /3 + C
 
Therefore, int (x+1)/sqrt(3x^2+6x)dx = sqrt(3x^2+6x) /3 + C .

Compare the characteristics of the spider woman with those of the old man.

The old man isn't actively pretending to be an angel, but due to his wings, he is certainly believed to be one by many. The spider woman, on the other hand, is a fraud, a charlatan, a confidence trickster. She immediately spots a gap in the market and exploits it to the fullest. She sees straightaway that the pilgrims who come to see her demand results from their faith, and she sets out to give them what they want.
Over time, the old man proves unable to perform the kind of wondrous miracles people expect from an angel. This creates an opportunity for the spider woman, who soon attracts visitors from far and wide, dispensing glib platitudes and passing them off as profound nuggets of wisdom. Here, Marquez appears to be satirizing a particular kind of folk-religion, one that is amenable to being exploited for personal gain by all manner of hucksters and con-artists.

The old man and the spider woman are similar in that they are both transgenic creatures. The old man is part human and part flying creature; perhaps he is an angel, but I don't believe that based on the existence of the spider woman. If a woman can exist that is part spider and part human, then I think a part human and part bird creature also makes sense. A physical difference between the two is their percentage of the other creature. The old man is described to us as an old man that happens to have wings. That contrasts sharply with the spider woman. She is mostly a spider that happens to have the head of a human. This difference is even indicated in their names. He is an old man with wings; the human part leads. The other is a spider with a human head; the non-human part leads. Another key difference is that the spider woman is completely able to share her story and willing to do so. The old man with wings is unable to communicate his story. It's either because he speaks a language that nobody understands or because he is simply making unintelligible noises.

Gabriel García Márquez provides a comparison between the spider woman and the old man with wings in his story “The Very Old Man with Enormous Wings.” When comparing the two characters it is important to remember the genre is magical realism.
The old man, who has a pair of feather wings growing out of his back, appears after a storm at sea. He is unable to communicate because he speaks in an unfamiliar seafarer’s dialect. There seems to be no rhyme or reason to his existence. The members of the small community think he is an angel, but even the village priest is unable to verify this.  People pay to visit and gawk at the old man as he becomes a curiosity.  This makes Pelayo and Elisenda rich, prosperous people. At times he is kept as an animal and put on display, yet he seems to have some power over the well-being of Pelayo and Elisenda’s child. When the child is sick, the old man suffers until both he and the child recover.
The spider woman is also a curiosity who travels with a freak show. She can explain how her actions caused her to morph into an entity who is part woman, part spider. Her ability to tell the story of how she disobeyed her parents, and was turned into a being with the body of a large spider attached to a human head makes her captivating to those who listen to her story. This takes attention away from the old man with wings. People were drawn to her, and were willing to pay to hear her story, which is in contrast to the old man's inability to communicate his background.
In both cases, the characters contribute to the genre of magical realism.
 
 

What happened to the men who originally found the silver mine?

The discovery of the silver mine corrupts those men who find it. The inn-keeper figures that, as he's so rich and no longer has to work, he can spend all day drinking. One night, the drunken inn-keeper drives off in his wagon, which overturns, killing him. The peasant Israel Per Persson mistakenly thinks that the silver is just glitter, so he sells his share of the silver to Olaf Sward—another one of the men who discovered the mine—for a relatively small sum of money. When the pastor tells Israel that the silver's real, the poor old peasant realizes his terrible mistake and weeps bitterly. As for Olaf himself, he gets into an argument with his brother Eric. The quarrel becomes violent and Olaf ends up killing Eric. For this serious crime, Olaf is sent to prison.
Given the great unhappiness that the silver mine has brought those who discovered it, it's not surprising that the pastor and the villagers make the decision to have the mine concealed forever. It has already ruined four good men, and human nature being what it is, it would almost certainly ruin a good many more.

Will the war in Afghanistan ever end?

It is impossible to say whether hostilities will cease in Afghanistan, but we can look at some of the barriers to peace and speculate accordingly. There are three groups operating in Afghanistan, each with its own objectives.
The Government of National Unity under President Ashraf Ghani wants to bring all Afghans under the central government in Kabul, which would end the civil war and work to mitigate social and religious differences among Afghan citizens.
The Taliban has stated that unity is possible, but not until American forces are out of the country.
The United States wants to maintain a military presence until it can be assured that Afghanistan will never again be the base for terrorist groups like Al-Qaeda.
As of March, 2018, the process for peace would be a five-year period that would probably involve all three parties meeting certain conditions.
The central government would set aside a specific number of provincial government positions for Taliban leaders to ensure Taliban interests are represented in Kabul.
In exchange, the Taliban would begin to draw down its military wing until it became a political party instead of an opposition regime.
As the changes began inside the Afghan government and the Taliban made good on its promise to demilitarize, the US military would withdraw to be replaced with NATO peacekeepers, who would eventually be removed completely.
The Taliban has erected a giant hurdle by saying that unity will never be an option as long as American soldiers remain on Afghan soil. Many see the Taliban walking back this position, but only if there is no risk of losing face.
https://thediplomat.com/2017/12/afghanistan-in-2017-achievements-and-challenges/

Single Variable Calculus, Chapter 3, 3.9, Section 3.9, Problem 6

Determine the Linear Approximation of the function $g(x) = \sqrt{1 + x}$ at $a = 0$ and use it to approximate the numbers $\sqrt[3]{0.95}$ and $\sqrt[3]{1.1}$. Illustrate by graphing $g$ and the tangent line.

Using the Linear Approximation/Tangent Line Approximation

$L(x) = f(a) + f'(a)(x - a)$


$
\begin{equation}
\begin{aligned}

f(a) = f(0) =& \sqrt[3]{1 + 0}
\\
\\
f(0) =& \sqrt[3]{1}
\\
\\
f(0) =& 1
\\
\\
f'(a) = f'(0) =& \frac{d}{dx} (\sqrt[3]{\sqrt{1 + x}})
\\
\\
f'(0) =& \frac{d}{dx} (1 + x)^{\frac{1}{3}}
\\
\\
f'(0) =& \frac{1}{3} (1 + x)^{\frac{-2}{3}}
\\
\\
f'(0) =& \frac{1}{3 (1 + x)^{\frac{2}{3}}}
\\
\\
f'(0) =& \frac{1}{3 (1 + 0)^{\frac{2}{3}}}
\\
\\
f'(0) =& \frac{1}{3(1)^{\frac{2}{3}}}
\\
\\
f'(0) =& \frac{1}{3}
\\
\\
L(x) =& 1 + \frac{1}{3} (x - 0)
\\
\\
L(x) =& 1 + \frac{1}{3} x

\end{aligned}
\end{equation}
$


For $\sqrt[3]{0.95}$


$
\begin{equation}
\begin{aligned}

\sqrt[3]{0.95} =& \sqrt[3]{1 + x}
\\
\\
0.95 =& 1 + x
\\
\\
x =& 0.95 - 1
\\
\\
x =& -0.05

\end{aligned}
\end{equation}
$


For $\sqrt{\sqrt[3]{1.1}}$


$
\begin{equation}
\begin{aligned}

\sqrt[3]{1.1} = \sqrt[3]{1 + x}
\\
\\
1.1 =& 1 + x
\\
\\
x =& 1.1 - 1
\\
\\
x =& 0.1

\end{aligned}
\end{equation}
$


Linear Approximation gives


$
\begin{equation}
\begin{aligned}

L(-0.05) =& 1 + \frac{1}{3} (-0.05)
\\
\\
L(-0.05) =& \frac{3 + (-0.05)}{3}
\\
\\
L(-0.05) =& \frac{3 - 0.05}{3}
\\
\\
L(-0.05) =& \frac{2.95}{3}
\\
\\
L(-0.05) =& 0.983

\end{aligned}
\end{equation}
$


and


$
\begin{equation}
\begin{aligned}

L(0.1) =& 1 + \frac{1}{3} (0.1)
\\
\\
L(0.1) =& \frac{3 + 0.1}{3}
\\
\\
L(0.1) =& \frac{3.1}{3}
\\
\\
L(0.1) =& 1.033

\end{aligned}
\end{equation}
$

In "The Seven Ages of Man," why does the speaker compare "reputation" to a "bubble"?

Jaques seems to be saying that reputation for valor is fleeting. It is something that looks impressive like a large bubble, but it can vanish in an instant like a bursting bubble. Shakespeare expresses a very similar notion in another play, Troilus and Cressida. In that play Achilles has refused to fight because he feels insulted by Agamemnon. Ulysses is trying to persuade Achilles to engage in battle again because he is such a great warrior and so badly needed by the Greeks. Ulysses works on Achilles' pride by getting the other leaders to ignore him and to pretend to be honoring Ajax as their great hero. Ulysses tells Achilles, in effect, that what you have done in the past is quickly forgotten; you have to keep accomplishing new deeds if you want your reputation to remain bright. That is the essence of what Ulysses tells Achilles in a long speech beginning with the following lines.

Time hath, my lord, a wallet at his back,Wherein he puts alms for oblivion,A great-siz'd monster of ingratitudes.Those scraps are good deeds past, which are devour'dAs fast as they are made, forgot as soonAs done. Perseverance, dear my lord,Keeps honour bright. To have done is to hangQuite out of fashion, like a rusty mailIn monumental mock'ry.      Act III, Scene 3

This is what Jaques is implying when he speaks of the "bubble reputation" in As You Like It. Reputation doesn't last. Therefore, according to Jaques, it isn't worth seeking. He believes that a soldier is foolish to look for something so fragile and valueless at great risk to his own life.

Seeking the bubble reputationEven in the cannon's mouth.    Act II, Scene 7

What evidence is there that Gatsby still lacks the background to attract a person from Daisy’s social class, despite his wealth in The Great Gatsby?

The rejection of the Sloanes in Chapter Six of The Great Gatsby evinces the rejection of Jay Gatsby by the upper class of East Egg who have "background."
After having arranged for Gatsby to meet Daisy at his cottage, Nick does not see either one for a while. But one Sunday Nick stops to visit Gatsby and is surprised to find Tom Buchanan there along with Mr. and Mrs. Sloane as they all have been out riding their horses. Nervously, Gatsby informs Tom that he knows Daisy; then, he invites Tom and the Sloanes to remain for dinner, but they decline. As the others converse, the Sloanes do not enter the conversation; however, after Mrs. Sloane has a couple of drinks, she says, "We'll all come to your next party, Mr. Gatsby." Gatsby expresses delight that they will come. Then, he suggests that Tom and the Sloanes stay for supper. When Mrs. Sloane says, "You come to supper with me," her husband says "Come along" to her only.

Gatsby looked at me questioningly. He wanted to go and he didn't see that Mr. Sloane had determined he shouldn't.

When everyone but Gatsby goes outside, Mr. Sloane takes his wife aside and has a private "impassioned conversation" with her.

"My God, I believe the man's coming," said Tom. "Doesn't he know she doesn't want him?"

Tom and the Sloanes mount their horses and start to go, but not before Gatsby, who has no horse, has said he will follow them in his car. But, just as he steps outside with his light overcoat and hat, he realizes that they have quickly trotted away. Thus, it is apparent that Gatsby is not of the same social class as the Sloanes, and he will not be socially acceptable at their "big dinner party [where] he won't know a soul...." as Mr. Sloane has said.
Tom also wonders how someone like Jay Gatsby would know Daisy. Of course, the truth is that Gatsby of West Egg, Long Island, "sprang from his Platonic conception of himself" and is not accepted by the social class of East Egg. 

What does the final line suggest about Dr. Pappenheim and the town of Badenheim?

Aharon Appelfeld's novel Badenheim 1939 is considered the "greatest novel of the Holocaust." The book focuses on the Austrian resort town of Badenheim and the changes that occur there in 1939 when Nazi forces, referred to as the "Sanitation Department," move in and begin to deconstruct the city in preparation for the forced deportation of the Jewish population to concentration camps. 
The book ends with the following line:
Nevertheless Dr. Pappenheim found time to make the following remark: "If the coaches are so dirty it must mean that we have not far to go." 
This line, in which the Jewish residents of the town are about to be deported, paints a stark portrait of what is to come. In the moments proceeding this, the people of the town are gathering at the station and observing their former homes, which look like "little pieces of folded cardboard." There is a sense of the unreal that abounds, as the townspeople do not have the dramatically ironic perspective that we, the readers, have in knowing that they are about to be sent to concentration camps. There they will face horrible torture, starvation, and death. 
The engine pulls into the station with four filthy freight cars attached to it, looking "as if it had risen from a pit in the ground," and the townspeople are ordered to board it. It is at this point that Dr. Pappenheim makes his aforementioned remark. 
This choice of words creates an effective—and disturbing—sense of just how delusional Dr. Pappenheim is. Although the novel depicts this man, who is responsible for organizing the annual music festival in Badenheim, as optimistic and rather eccentric, this final prediction of his borders on the absurd. Dr. Pappenheim falsely believes that what the Jews face in being deported to Poland is an adventure which will bring them to a new life in an exciting foreign land; his idealism causes him to ignore the glaringly obvious, ominous signals that surround him. Much of his energy is spent denying reality rather than building resilience for what he is about to encounter. When faced with the final symbol of the destruction of the Jews—the freight cars—Dr. Pappenheim misinterprets it, suggesting that he is still ignorant to the cultural, religious, and ethnic war that is about to explode around him. 

What three traits with three different types of evidence explain Dave Parker in the book No Talking by Andrew Clements? What three traits does Dave Parker have in the book No Talking by Andrew Clements? What is the evidence?

One character trait of Dave Parker's in Andrew Clements' No Talking is leadership The narrator describes both Dave and Lysnsey as leaders when the narrator points out early in the story that both were the "king and queen of the fifth-grade cootie-clingers," which means they were the leaders of their fifth-grade class. Dave shows leadership skills by thinking up the contest. Leaders must be very creative thinkers, and thinking of a contest to see if boys or girls could talk less is certainly a very creative way to put an end to the conflict he created between himself and Lynsey by insulting her talking habits. Dave also thinks creatively, like a leader, when he thinks of rules for the contest such as the rule that contractions, if found in the dictionary, can count as one word.A second characteristic Dave has is bravery, which is also a characteristic leaders have. Dave demonstrates bravery when he keeps up his vow of silence even in the face of authority figures. For example, when he knows his mother is getting worried because he won't answer her from the bathroom, he very bravely finds a way to pacify the situation by opening the door as quickly as possible, hugging her, and telling her in writing about the contest. Dave best demonstrates bravery when he stands up to Mrs. Hiatt's bullying. Mrs. Hiatt, the school principal, is upset that the kids aren't talking because it's too far out of the ordinary. When she commands them to talk and they refuse, she gets angered because she thinks they are disrespecting her. She gets so angry that she yells at Dave through her bullhorn, which Dave rightly sees as unnecessary and as a form of bullying. In response, he yells right back and defends their "right to remain silentita" (p. 108). Since it takes a lot of bravery to stand up to a school principal, Dave's action shows us just how brave he is, just like any leader.

Calculus: Early Transcendentals, Chapter 5, 5.4, Section 5.4, Problem 39

We will make substitution x=t^6. Therefore, the differential is dx=6t^5dt and the new bounds of integration are t_1=root(6)(1)=1 and t_2=root(6)(64)=2.
int_1^64(1+root(3)(x))/sqrt x dx=int_1^2((1+t^2)6t^5)/t^3dt=6int_1^2(1+t^2)t^2dt=6int_1^2(t^2+t^4)dt=
6(t^3/3+t^5/5)|_1^2=6(8/3+32/5-1/3-1/5)=6\cdot128/15=256/5 <-- The solution

Who told Swift about the use of children as a source of food?

One proposed source for Swift's satiric essay is John Locke's First Treatise on Government, in which Locke writes of people in ancient societies doing this:

Be it then as Sir Robert says, that Anciently, it was usual for Men to sell and Castrate their Children. Let it be, that they exposed them; Add to it, if you please, for this is still greater Power, that they begat them for their Tables to fat and eat them . . .

In the essay itself, the clueless narrator, who should not be confused with Swift, mentions twice an American acquaintance who has discussed with him how tasty and wholesome a one-year-old child is and how tough the flesh of an older child of about twelve is. While this doesn't offer a specific source for the essay, it plays on exotic tales of cannibalism in the Americas.
While Swift did model his essay on Roman satires, what is striking about it is how original it is: it is in its over-the-top idea of eating children, presented as if it makes logical sense, that the shock value lies. Mostly, the essay arises from Swift's upset over the suffering of the Irish and the unwillingness of their English overlords to make the least sacrifice to alleviate the distressing situation. As the narrator puts it in the essay, saying more than he realizes:

I grant this food will be somewhat dear, and therefore very proper for landlords, who, as they have already devoured most of the parents, seem to have the best title to the children.

Tom makes the mistake of bringing up his previous love, Amy Lawrence, which causes Becky to cry. Briefly explain.

Becky is crying because she's insanely jealous of Tom's previous girlfriend. Tom has led Becky to believe that getting engaged is a big deal and that it only happens between people who really care about each other. But the fact that he's been engaged before to his first love, Amy Lawrence, indicates that this isn't the case for Tom. It's obvious to Becky that getting engaged isn't something that Tom takes seriously at all.
In fairness to Tom, he's still just a child and so has no real understanding of what getting engaged actually entails. He's far too young to understand its true significance and the incredible commitment required. But then Becky doesn't really understand what it's all about, either. One thing she does understand is that she no longer feels that she really matters to Tom, so she cries her eyes out.

Just prior to Becky Thatcher’s crying, Tom had asked her to get “engaged” to him. In Tom’s explanation, being engaged means promising that you will never love anybody else but the person to which you are engaged.
Understandably, Becky takes this to mean that Tom is very serious about his love for her and that she is special. When Tom ignorantly talks about being previously engaged, Becky is overcome with jealousy. She interprets Tom’s prior engagement as proof that he does not truly love her and that she is indeed unremarkable to him.
It helps to understand that both Tom and Becky are children, so their emotions are not regulated as well as adults, and their understanding of love and romance is limited. In Becky’s mind, it’s almost as if Tom has cheated on her because he had liked another girl before her. While this makes no sense from a mature perspective, it is a serious transgression for Becky. She feels betrayed and heartbroken in this moment because she can’t believe Tom has already been “engaged” before.

What is the universal idea of "I Sing the Body Electric"?

I assume this question is asking about which universal themes are present in Whitman's "I Sing the Body Electric," or about how Whitman explores the universality of the body in this poem.
For some context, Whitman was a humanist, which means that he valued freedom and agency in human beings, both as individuals and as a collective. This poem (and other poems in Leaves of Grass) explores the physicality and the sacred qualities of being a human being. Whitman tells us in part 8, "If any thing is sacred the human body is sacred..." 
One universal idea in "I Sing the Body Electric" is the idea that all bodies are equal. Through his use of lists and catalogues throughout the poem, Whitman places descriptions of many different kinds of bodies side by side. In listing these different bodies, he gives them all equal value and attention. After describing the female form, Whitman writes in part 6, "The male is not less the soul nor more, he too is in his place, / He too is all qualities, he is action and power..." He also tells us in part 6, "The man’s body is sacred and the woman’s body is sacred, / No matter who it is, it is sacred...." Whitman believes that male and female bodies are equally important. Other bodies that Whitman explores are those of farmers and of slaves, as well as the speaker's own body. He repeatedly emphasizes that these bodies are equal.
Another universal idea present in the poem is the idea that human bodies refuse neat categorization or labels. In part 2, Whitman writes: "The love of the body of man or woman balks account, the body itself balks account, / That of the male is perfect, and that of the female is perfect." Thus, Whitman tells us that even though he's about to describe the physical body, he understands, and we should understand, too, that the human body resists categorization. Whitman implies that sometimes we are unable to use language to truly capture the human body in its entirety. 

What do you think might have happened had Indians been immune to the germs introduced to them by the Europeans?

Diseases brought by Europeans took a great toll on Native Americans, who had not built up the same immunities as the Europeans. Smallpox was particularly deadly, but diseases such as measles, typhoid, tuberculosis, the common cold, scarlet fever, and whooping cough also took a toll. According to Carl Waldman Atlas of the North American Indian, between a quarter and half of the Native American population was destroyed by disease after first contact with Europeans. In some cases, the numbers were much higher. According to K.E. Nielsen's A Disability History of the United States, more than 90 percent of Florida's Native American population succumbed to disease by 1700.
It's not hard to see that, had the Indians been able to withstand the diseases brought by the Europeans—say, having been exposed to them in their own settings and developing immunity—they would have been better able to resist the Europeans taking their lands. Further, the levels of death caused by disease would have been traumatic, leaving the Natives Americans psychologically stunned. Without the trauma of disease, the native population would have been less psychologically vulnerable to conquest.
A larger native population probably would still have fallen short of the number of Europeans coming to its shore, but the natives would have possessed significant advantages in knowledge of the terrain. One can easily imagine that "manifest destiny" would not have seemed so obvious to the European settlers. Having more threat of warfare from a larger population of Native Americans would probably have led the Europeans to be more careful about honoring treaties and more willing to negotiate with the natives in good faith. It also would have meant, however, being faced with fiercer battling for each hunk of territory. The Europeans would very likely have managed to be satisfied with less land and a more respectful coexistent with their Indian neighbors. Wars would have been more costly, and European governments thus less likely to want to engage in them. The North American continent today might look more like a patchwork of native and former European nations rather than an English-speaking monolith.

Are there any strategies that could reduce the threat that the world's population may eventually not be able to sustain itself and its environment?

The issue you are concerned about was actually first raised by the English clergyman, the Reverend Thomas Malthus, who noted in the late eighteenth century that the population was growing geometrically but food supplies were only growing arithmetically, and predicted this would eventually lead to a crisis in which food supplies were inadequate to feed the world population. There are two possible solutions to this problem: reducing population or reducing the environmental impact of each person.
There are several ways to reduce the population. The first is government incentives ranging from the authoritarian (China's one-child policies) to various more subtle incentives, such as eliminating tax breaks and other forms of subsidies for bearing children and increased incentives or tax breaks for not having children. Access to free birth control, abortion, and sterilization also allows people to choose not to have children. Another major step in reducing population growth is educating women, increasing gender equality, and reducing poverty, as better-educated women in countries with less poverty and more equality of opportunity tend to bear fewer children.
There are several ways to reduce the environmental impact of individuals, including recycling, using renewable energies, reducing use of fossil fuels, and implementing other green initiatives. There are several strategies to increase agricultural yields in a sustainable fashion. One of the most obvious ways to increase food supply is for people to follow vegetarian diets, as it takes 8 to 30 pounds of plant food to create a pound of meat; it is much more efficient for people simply to eat plants rather than feed plants to animals and then eat animals. 

How did industrialization effect the Indian cotton handicrafts?

Cotton was an important crop in India.  This cotton was turned into spun thread and woven by hand.  The cloth created by woven Indian cotton was cool and lightweight.  This made it especially popular in England.  Often it was dyed beautiful colors.  
In India, all of the harvesting, spinning of the thread, weaving of the cloth, and dying of the finished product was done meticulously by hand.  The workers who did these processes were skilled.  With the arrival Industrial Revolution, it became cheaper to make cotton cloth using large factory machinery instead of by hand.  This had a negative impact on the people who wove cotton cloth by hand in India.  On top of this, the United States had already become the main center for cotton production in the world.  England had already begun purchasing cotton from the United States instead of India.
Before cotton could even be produced into cloth and other goods, the seeds needed to be removed.  With the invention of the cotton gin, speeds could be removed by machine.  This strengthened the cotton trade in North America.  The Indian cotton industry operated locally, rather than on a larger, more organized scale.  This caused further decline and had a negative impact on the Indian cotton handicraft industry.

Ponyboy is confused about the different treatment his friends give girls. Explain what he means. Give an example of how this is true.

In The Outsiders, Ponyboy is "confused" about his friends' behavior to girls. This is likely because he sees his friends exhibiting both respectful and disrespectful attitudes. In one case, his brother Soda wants to marry Sandy, despite the fact that Sandy is pregnant with a different partner's child. This suggests that Soda's appreciation for Sandy goes beyond the superficial; he respects her as a companion. Contrast this with the behavior Ponyboy witnesses toward Cherry and Marcia at the drive in. First, Dallas harasses them, diminishing them to their physical appearance. Then, the two girls seem to decide to spend the evening with the Greasers before being "claimed" by their Soc boyfriends, Bob and Randy. This incident suggests that girls are objects, or prizes to be passed around between their male counterparts for social status. Over the course of the novel, Ponyboy sees girls treated sometimes respectfully, sometimes as sexual objects, and sometimes as trophies—confusing indeed!

What was Louis Napoleon Bonaparte's nationalist response to rising to power?

Louis Napoleon Bonaparte, otherwise known as Napoleon III, was a fascinating figure. Jailed as a result of a failed coup attempt in the 1830s, Louis Napoleon escaped from prison in the 1840s and found his way into France's National Assembly in the chaos of the Revolution of 1848. Over the next couple of years he coalesced his power and became President of the Second Republic. Ever ambitious, he manufactured a coup d'état in 1851, which led to the formation of the Second Empire. This political maneuvering is famously documented by Marx in his essay The Eighteenth Brumaire of Louis Napoleon (1852).
Napoleon III was a champion of nationalism. In addition to increasing national pride in France itself through his famous public works projects in the 1850s and 60s overseen by Baron Haussmann, he also sponsored nationalist objectives in other contexts. He supported Italian nationalism in the 1860s. Increasing the scale of France's international involvement, he doubled the size of its overseas empire.
Finally, his attempt to champion French national pride got him involved in the Franco-Prussian War in 1870, which led to major military defeats and the end of his Empire. He went into exile and died a couple of years later.

In the film Ken Burns: Central Park Five, why do you think the boys falsely confessed? What factors of the interrogation process and/or personal factors contributed?

In 1989, a woman jogging through Central Park in New York was brutally raped and almost murdered.  Until 2002, when convicted murderer and rapist Mathias Reyes confessed to the rape, the police believed that they had solved the crime.  They brought in five black or Latino teenagers, aged 14 to 16, and interrogated them.  At the time, all five of them confessed to having been involved.  But why would all five of them confess to the crime when clearly all five of them did not commit the crime?  And why would the police allow this to happen?  
There are many reasons why false confessions happen.  Sometimes interrogators may promise a lighter sentence to a suspect who confesses. Investigators might also use psychological terror to make someone feel guilty and afraid.  The young and inexperienced—like the five boys in question—are particularly vulnerable to these tactics.  The police can also tell a suspect that they already have evidence to link that suspect to the crime, leading the suspect to believe it would be in their best interest to confess. When you're a 14- to 16-year-old boy being interrogated by NYC detectives and policemen, however, nothing can prepare you for the psychological torture that thirty hours of interrogation can put you through.  Sometimes, confessing might seem like the least stressful option.
According to psychologists who have studied the case, people, especially young people, can become so broken down during these interrogations that they come to the counterintuitive conclusion that confessing is in their best interest. Because many are unaware that interrogators are legally permitted to lie about any and all types of evidence, including DNA evidence, prints found at the scene, and polygraph test results, suspects may end up believing that their conviction is a foregone conclusion and that they should confess to reduce or otherwise improve their sentence.  Some may even become so confused and frightened that they confess simply to make the torturous interrogation stop.  That the boys in question were young and belonged to minority ethnic groups that have traditionally been subject to prejudice and disproportionate rates of incarceration might be evidence that the boys believed the legal system would not work in their favor—regardless of whether they were innocent or not. 
Interestingly, none of them ever confessed to committing the crime themselves; they all implicated the others.  They were all coerced confessions in the case of the Central Park Five, because they were led to believe that if they confessed, they could go home.  And what teenager doesn't want that? What the police failed to mention before the trial, however, was that the DNA test results came back from the lab, all implicating a single individual that wasn't any of the accused boys.  The police believed that they could get a conviction based on the assumption that they were somehow still involved, and that maybe there was an unnamed sixth individual that they didn't catch.  
It's very difficult for a judge or jury to look past a confession, no matter what the circumstances surrounding it are. Many times they have no access to the interrogation process. In fact, in his book about the phenomenon of false confessions, law professor Brandon L. Garrett found that

"...in many of the cases the defendants were young or mentally disabled. In none were the interrogations recorded, making it difficult to know what manipulative and coercive measures the police used."

This is a huge issue surrounding our justice system today.  According to experts, police exercise an extreme amount of power in these cases—arguably too much power. They can lie about evidence, they can use psychological torture, they don't have to tape the confession, etc. A suspect's only option can seem to be confessing or blaming someone else for the crime while admitting that they still played a part. This is what the Central Park Five did. For these reasons, the Central Park Five were convicted on false confessions and served up to thirteen years in prison for crimes that they didn't commit.
http://ideas.time.com/2013/02/11/why-innocent-men-make-false-confessions/

http://thepsychreport.com/conversations/coerced-to-confess-the-psychology-of-false-confessions/

What does Aram experience when he tries to ride the white horse in "The Summer of the Beautiful White Horse" by Saroyan?

Aram encounters a number of experiences while riding the horse in the short story “The Summer of the Beautiful White Horse” by William Saroyan.
When his cousin arrives with the horse in the early morning, Aram is filled with excitement and disbelief. He expresses his feelings by saying, “In the first place, my earliest memories had been memories of horses and my first longings had been longings to ride.”
Mourad encourages him to hurry, and the two ride the white horse together. As they ride, they allow the horse to free rein, and he runs at his pleasure.

We rode and my cousin Mourad sang. For all anybody knew we were still in the old country where, at least according to some of our neighbors, we belonged. We let the horse run as long as it felt like running.

Mourad orders Aram to dismount and allow him to ride alone. Aram questions whether he can ride alone when his cousin is finished.

At last my cousin Mourad said, Get down. I want to ride alone.
Will you let me ride alone? I said.
That is up to the horse, my cousin said. Get down.
The horse will let me ride, I said.
We shall see, he said. Don't forget that I have a way with a horse.

As Aram watches Mourad ride, he is filled with anticipation and the belief that he, too, has a way with the animal. Finally, Mourad allows him to mount the horse but the ride does not go as expected.
Aram, filled with fear, mounts the horse, who does not move. His cousin encourages him to kick the animal in its muscles, which causes the horse to race off. For a time, Aram is able to hang on as the horse runs wildly through a vineyard, jumping over the vines, until he is thrown from the horse, who gallops away. The pair search for more than thirty minutes before finding and cornering the animal.

Which major themes of history have defined the era of 1804–1939?

In my view, the most important themes of the period 1804–1939 were nationalism, independence, industrialization, and globalization, each of which was related to and intertwined with the others.
1804 marked the start of Napoleon's period of greatest power. He had himself crowned Emperor and then embarked on a successful campaign in the heart of Europe, defeating the Austrians, Russians, and Prussians, bringing an end to the Holy Roman Empire and the old order of Europe. He reduced the German principalities to client states and compelled Russia into an initial alliance with France. All of this, however, stimulated nationalistic resentment, an ethnic "awakening," particularly among the Germans, and an eventual rising against Napoleon's dominance.The huge battle that took place at Leipzig in 1813 is known in German as the Völkerschlacht (battle of the nations), which signaled the beginning of the end for Napoleon and the breakup of his empire. German leaders who were at first allied with Napoleon switched sides in the course of the long battle. After Bonaparte's final defeat, nationalism eventually led to the desire to create unified nation-states. Italy was unified in 1870 and Germany in 1871.
A corollary of nationalism is the desire for independence from foreign or colonial rule. The Latin American countries achieved this in the 1820s. In the same decade, Greece, with help from Western Europe, became independent of the Ottoman Empire, as did most of the Balkan peoples by 1913. Yet during the nineteenth century, European imperialism and dominance over non-European peoples increased. India was made an official part of the British Empire instead of merely a "possession" of the East India Company. Imperialism wasn't just a British issue—France, Belgium, the Netherlands, Italy, and Germany all got into the imperialism game with colonies in Asia and Africa. This situation persisted until the end of the period we are examining and beyond.
Independence as a concept includes the liberation of unfree peoples in the labor force. By the 1860s, serfdom had been finally abolished in all of Europe. Slavery was ended in 1865 in the US and in Brazil by the 1890s. Industrialization in Europe and North America resulted in large population shifts from the countryside to the cities. In Europe, rural people were largely forced off the land by "enclosures" and the expropriation of land by the owning classes. By the late nineteenth century and into the early twentieth, unions were created in the Western countries, which partly ameliorated the exploitation of labor and improved conditions for workers. Ironically, it was the country in Europe with the least industry, Russia, which saw in 1917 a revolution in which the ruling class was expelled, though the Bolsheviks who took over ended up oppressing the population even more severely than the Czarist regime had done.
The forces of nationalism, the wish to redress past grievances, and economic competition among the colonial European powers—in particular, a shift in the balance of power caused by the recently unified Germany—led to the explosion of 1914. World War I proved to be the deadliest war in European history to that point. In its aftermath, the Austrian, Ottoman, and Russian empires were dissolved. The resentment in Germany over the terms of the Armistice and the indemnity imposed on Germany was exploited by Hitler to achieve power and create the brutal, genocidal dictatorship that started World War II in 1939.
In the meantime, a globalization process was occurring that tied into these developments. Advances in technology and communication began to erode the insular character (with regard to the West) of both China and Japan. After the Meiji restoration in Japan in 1868, the Japanese entered a process of modernization. British and American military experts were brought in to create a Western-style army. Japan began to have imperialistic ambitions and intended to create a vast empire in Asia, first invading China and then attempting to expel the Western powers from Asia beginning in 1941. Though the Japanese were defeated, of course, World War II simultaneously marked the beginning of the end for colonialism in Asia and throughout the world as a whole.

How did Macbeth become a loyal servant to King Duncan?

Macbeth is renowned as a brave and valiant warrior. He shows his immense courage, as well as his loyalty to King Duncan, on the field of battle. As the play opens, Duncan's enemies have just been comprehensively routed, with Macbeth more responsible than anyone else for Duncan's decisive military triumph. Ironically, Duncan rewards Macbeth for his loyalty by making him Thane of Cawdor (the previous holder of that title has been executed as a traitor).
Yet Macbeth in due course will stoop to much greater depths of treachery and deceit than the previous Thane. His actions are made all the more shocking by the fact that he starts off as such an unfailingly loyal and honorable servant of his king. Macbeth's the very last person that anyone would suspect of having designs on Duncan's throne. After all, his loyalty has paid off; he's been rewarded by the title of Thane of Cawdor. There's simply no need for him to get any ideas about stabbing Duncan in the back. That he subsequently does betray Duncan serves to develop the important themes of loyalty and betrayal, as well as driving the plot forward.

Single Variable Calculus, Chapter 3, 3.9, Section 3.9, Problem 14

a.) Determine the differential of $\displaystyle y = (t + \tan t)^5$

Using Differential Approximation

$dy = f'(t) dt$


$
\begin{equation}
\begin{aligned}

\frac{dy}{dt} =& \frac{d}{dt} (t + \tan t)^5
\\
\\
dy =& \left[ 5 (t + \tan t)^4 \frac{d}{dt} (t + \tan t) \right] dt
\\
\\
dy =& 5(t + \tan t)^4 (1 + \sec^2 t) dt


\end{aligned}
\end{equation}
$


b.) Determine the differential of $\displaystyle y = \sqrt{z + \frac{1}{2}}$

Using Differential Approximation

$dy = f'(z) dz$


$
\begin{equation}
\begin{aligned}

\frac{dy}{dz} =& \left(z + \frac{1}{2}\right)^{\frac{1}{2}}
\\
\\
dy =& \left[ \frac{1}{2} + \left( z + \frac{1}{z} \right) ^{\frac{-1}{2}} \frac{d}{dz} \left( z + \frac{1}{z} \right) \right] dz
\\
\\
dy =& \left[ \frac{1}{2} \left( z + \frac{1}{z} \right) ^{\frac{-1}{2}} \left( 1 + \left( \frac{-1}{z^2}\right) \right) \right] dz
\\
\\
dy =& \left[ \left( \frac{1}{\displaystyle 2 (z + \frac{1}{z})^{\frac{1}{2}}} \right) \left( 1 - \frac{1}{z^2} \right) \right] dz
\\
\\
dy =& \left[ \left( \frac{1}{\displaystyle 2 \left( \frac{z^2 + 1}{z} \right)^{\frac{1}{2}}} \right) \left( \frac{z^2 - 1}{z^2} \right) \right] dz
\\
\\
dy =& \left[ \frac{z^2 - 1}{2z^2 \displaystyle \frac{(z^2 + 1)^{\frac{1}{2}}}{(z)^{\frac{1}{2}}}} \right] dz
\\
\\
dy =& \left[ \frac{z^2 - 1}{2 (z)^{\frac{3}{2}} (z^2 + 1)^{\frac{1}{2}}} \right] dz
\\
\\
dy =& \left[ \frac{z^2 - 1}{2(z)(z)^{\frac{1}{2}} (z^2 + 1)^{\frac{1}{2}}} \right] dz
\\
\\
dy =& \frac{z^2 - 1}{2z [z (z^2 + 1)^{\frac{1}{2}}]^{\frac{1}{2}}} dz
\\
\\
dy =& \frac{z^2 - 1}{2z (z^3 + z)^{\frac{1}{2}}} dz
\\
\\
& \text{ or }
\\
\\
dy =& \frac{z^2 - 1}{2z \sqrt{z^3 + z}} dz

\end{aligned}
\end{equation}
$

What are open vowels? Explain with examples.

To really understand the answer to this question, you will need to pronounce some sounds and pay attention to how they feel in your throat and mouth. (Are you in a private space and not, say, in the middle of the dining hall or a quiet library? Perfect! Let us continue.)
Vowels and consonants are the building blocks of speech sounds. Vowels are considered the nucleus of a syllable.
Vowels (A, E, I, O, U), by their very definition, are produced by an open use of the vocal tract. Go ahead, make the sound "a," as in the word "father." Notice how your mouth opens wide on that first syllable?
Now, try another word that has a different vowel: the letter "u." Say the word "tube." Do you notice how your mouth makes a completely different shape as you say it? It is not like the open, tall-mouthed feeling you have when you say the word "father," is it?
Nouns might all involve an open use of the vocal tract, but they are not all the same. What is an open vowel (also referred to as a low vowel)? In short, it is a vowel sound that you make with your tongue positioned as far away as possible from the roof of your mouth. The term "low vowel" is sometimes used, as I said, and "low" refers to the low position of the tongue in your mouth.
Examples: "ARM." "GOT." Say these words aloud and notice how your mouth is open "tall" as you produce the vowel sound.
In contrast, if your mouth is almost closed when you produce a vowel, you are pronouncing a "closed vowel."
Examples: "SEE." "TOO." Do you notice how your mouth barely opens to make these sounds?
If the vowel is somewhere in the middle, with your mouth open midway, that is considered a "mid vowel."
Examples: "CUP." "AGO." You open your mouth a little bit but not a lot.
Linguistics professors often use a chart to illustrate the different positions the tongue takes as we pronounce vowels. However, I personally find it a little abstract. I am attaching a different vowel space diagram that actually shows a cross-section of the human head and the positioning of the tongue in the mouth when pronouncing different kinds of vowels.
Of course, you can also just say a given word aloud and ask yourself whether it has an open, closed, or mid vowel.
https://notendur.hi.is/peturk/KENNSLA/02/TOP/VowelSpace.html

lim_(x->1^(+)) (int_1^x cos(theta) d theta ) / (x-1) Evaluate the limit, using L’Hôpital’s Rule if necessary.

 
Givne to solve,
lim_(x->1^(+)) (int_1^x cos(theta) d theta ) / (x-1)
=lim_(x->1^(+)) ([sin(theta)]_1^x) / (x-1)
=lim_(x->1^(+)) ([sin(x)-sin(1)]) / (x-1)
when x-> 1+ then ([sin(x)-sin(1)]) / (x-1) = 0/0 form
so upon applying the L 'Hopital rule we get the solution as follows,
as for the general equation it is as follows
lim_(x->a) f(x)/g(x) is = 0/0 or (+-oo)/(+-oo) then by using the L'Hopital Rule we get  the solution with the  below form.
lim_(x->a) (f'(x))/(g'(x))
 
so , now evaluating
lim_(x->1^(+)) ([sin(x)-sin(1)]) / (x-1)
=lim_(x->1^(+)) (([sin(x)-sin(1)])') / ((x-1)')
=lim_(x->1^(+)) (cos(x)) / (1)
=lim_(x->1^(+)) (cos(x))
on plugging the value x= 1
we get
lim_(x->1^(+)) (cos(x))
=cos(1)
 

The following sentence is ambiguous. Provide two explanations which illustrate the different meanings of the sentence. "Please make sure you take the right turn at the intersection."

The sentence is ambiguous because of the word "right." Right could refer to a direction of navigation, or it could refer to a correct choice.  
If somebody were to give you directions, and the intersections were confusing, the above sentence wouldn't necessarily tell you which direction to turn. I would hope that because the person is giving directions, "right" means a literal turn toward the right. In other words, don't go left.  
The ambiguity comes from the fact that the sentence might simply be telling you to make the correct choice at the intersection. If someone told you, "When you get to Broadway and 9th, take the correct path," whether that path is right, left, or straight is not indicated. It is assumed that the person knows the correct direction to navigate and doesn't need to be told in which direction to go. In my opinion, that's poor direction-giving. If I am giving somebody directions, I assume they don't know how to get somewhere. I will use "right" exclusively as a direction indicator. Occasionally, a person will repeat the directions back to me, and I am very careful with how I respond.
For example, the person might ask, "So, when I get to the corner of Ash and Lincoln, I go left?" If that is correct, I will say "correct." I will not say "right." If I say right, the person won't know if I am affirming them or correcting them.

The key word here is the adjective “right.” Which one of its meanings is used in this instructional sentence?
If “right” is used to mean “correct,” then this instruction could be considered almost a warning. The upcoming road crossing is complex. Please be sure to make only the correct and proper turn at this juncture. The implication is that if you don’t do so, you will get lost. Or at the very least, you will have to turn around and approach the crossing in the other direction and figure out from that point which way the “correct” way lies.
If “right” is used as a directional term, then it refers to the opposite of “left.” As you approach this complex road crossing, put on your right turn signal (if you are driving a car), and turn onto the road that lies just to your right. Again, the implication is that you may get lost if you don’t make this turn.

What do you think Marshall means in chapter 11 when he says, “somebody already heard us”?

Marshall knows that the children are being watched as they play the Egypt Game. The children are so engrossed by the imaginative game they've constructed that they're often unaware of what's going on around them. But Marshall is a lot less engaged in the game, and thus more observant of his immediate surroundings. He knows that the Professor has been watching the children from the window as they play their game in his storage yard.
As part of the game, April comes up with the bright idea of "sacrificing" Marshall's comfort toy. As one can imagine, Marshall' is not very happy at her suggestion. In fact, he's so mad that he screams. The girls try to get him to be quiet, and that's when Marshall tells them that somebody's already heard them, though he doesn't care to elaborate on what he means by that.

What social and political attitudes or traditions does Jane Austen wish to change in Emma?

Jane Austen's politics are highly contested (was she high Tory or secret radical sympathizer: see Marilyn Butler on Austen as Tory and the new book by Helena Kelly: Jane Austen: The Secret Radical for Austen as subversive.) While her politics may be ambiguous, we can locate places in the social order that Austen critiques in Emma. 
Austen's text builds sympathy for the plight of poorer gentry women. While Miss Bates is seen through Emma's eyes as ridiculous, we as readers are also shown a woman trying to survive in reduced circumstances who has been rendered ridiculous by a society that looks down on older, poorer, unmarried women (incidentally, Austen herself a single woman, would have been about Miss Bates's age at the time she wrote Emma.) In having Mr. Knightley scold Emma, and in having Emma herself recognize and repent of her cruelty in making a rude comment to Miss Bates at Box Hill, Austen critiques the casual verbal savagery that can make life a misery for women on the social periphery. Her novel at least suggests changes in attitudes and practices.
In making Jane Fairfax a sympathetic character, which she is even as we see her refracted through Emma's eyes, Austen again critiques a society that doesn't take care of poor gentry woman of intelligence, beauty, talent, and grace. Jane's fate is to become a governess, a career which entails social humiliation and which Jane equates to a form of slavery. Jane is "saved" from governessing through marriage to frivolous Frank Churchill, but implicit in the novel is the lack of choice for a talented woman like Jane.
Finally, Austen critiques snobbery. Emma's snobbery in trying to prevent Harriet Smith from marrying the farmer Robert Martin could have had dire consequences for Harriet, an illegitimate child with little money, no connections, and few prospects. Luckily, it all works out for Harriet, but the reader can easily see, if Emma cannot, how snobbery could have ruined Harriet's prospects.

How does the hotel scene enhance the conflict between classes in chapter 7 of The Great Gatsby?

Tom dismissively calls Gatsby "'Mr. Nobody from Nowhere,'" and he suggests that Gatsby is "'sneering at family life and family institutions'" by trying to break up his family. Family is important to most social groups; however, it was especially important financially to the old moneyed upper-class who inherited their fortunes rather than worked for them. When Tom references family institutions and life, he seems to be both snobbishly criticizing Gatsby for having no important family, no family that could leave him a fortune to inherit, as well as holding up his own family as the ideal kind. Gatsby is no one from nowhere, but Tom is a Buchanan, with a Yale education and a string of polo ponies and a white palace in East Egg. Tom suggests that Gatsby turns his "'house into a pigsty'" just to make friends; Tom, of course, doesn't have to do that. His class comes with friends; like mixes with like. He feels like Gatsby has no right to be anywhere near himself or his wife, and he makes it clear.

At the Plaza Hotel, Gatsby and Tom Buchanan face off over Daisy. Tom does everything he can to press his class advantage over his rival. First, Tom, a Yale graduate, taunts Gatsby over allegedly being an "Oxford man," which Tom does not believe for a minute. When Gatsby explains that he was only there for five months as part of a World War I armistice opportunity that allowed some officers to study at Oxford, Nick's faith in Gatsby is restored. But upper crust Tom keeps on relentlessly pushing the "class warfare" theme, saying that if Gatsby can make love to Daisy, the next thing will be "intermarriage between black and white." Finally, he says that someone like Gatsby should not be allowed "within a mile" of Daisy unless he is delivering groceries to the back door like a servant. We've known from the beginning that Tom is a snob, but here he openly uses his conviction that Gatsby is lower class to try to separate Daisy and Gatsby. 

The mantra "bigger is better" has been touted for centuries. In today's modern world, is bigger really better when it comes to food?

The notion that bigger is better is problematic in many respects; however, it is particularly problematic with regard to food. For one, industrial-sized farming operations incur tremendous environmental costs because they use large amounts of water and contribute to global warming. Industrial meat and dairy production, for example, has been implicated as one of the leading sources of CO2-emissions worldwide.  
Secondly, big portion sizes, especially of highly processed foods, have long been implicated as being a major contributor to the obesity epidemic. The Centers for Disease Control and Prevention (CDC) estimate that 36.5% of Americans are obese. This is a public health crisis because obesity is associated with a host of other diseases including heart disease, Type 2 diabetes and cancer. Apart from increased healthcare costs caused by treating obese patients, people also experience reduced quality of life due to these diseases.  
So overall, when it comes to food, bigger is definitively not always better.
https://www.cdc.gov/obesity/data/adult.html

Calculus: Early Transcendentals, Chapter 7, 7.4, Section 7.4, Problem 15

int_3^4 (x^3-2x^2 - 4)/(x^3 - 2x^2) dx
First we will solve
int (x^3-2x^2 - 4)/(x^3 - 2x^2) dx , then we can apply the limits
=int (x^3-2x^2 - 4)/(x^3 - 2x^2) dx
=int [1- (4/(x^3 - 2x^2)) dx
= int 1 dx - int (4/(x^3 - 2x^2)) dx
= x - 4*int (1/(x^2(x - 2)) dx
1/(x^2(x - 2)) on partial fraction we get
1/((x^2(x - 2)) = ((-1)/4x))+((-1)/(2x^2))+(1/(4(x-2)))
so ,
= x - [4*int (1/(x^2(x - 2)) ] dx
= x-[4*int [((-1)/4x))+((-1)/(2x^2))+(1/(4(x-2)))] dx
= x- [4*int ((-1)/4x))dx+ 4*int((-1)/(2x^2)) dx+ 4*int(1/(4(x-2)))] dx
= x -[4*(-ln(x)/4)+4* (1/(2x)) +4*(ln(x-2)/4)] +c
= x + 4*(ln(x)/4) - 4* (1/(2x)) - 4*(ln(x-2)/4)] +c
so ,
int (x^3-2x^2 - 4)/(x^3 - 2x^2) dx =x + 4*(ln(x)/4) - 4* (1/(2x)) - 4*(ln(x-2)/4)] +c
now,
int_3^4 (x^3-2x^2 - 4)/(x^3 - 2x^2) dx
= [x + 4*(ln(x)/4) - 4* (1/(2x)) - 4*(ln(x-2)/4) ]_3^4
= [4 +(ln(4)) -2* (1/(4)) - (ln(4-2)) ]-[3 +(ln(3))-2* (1/(3)) - (ln(3-2)) ]
=[4 +2*(ln(2))- (1/(2)) - (ln(2)) ]-[3 +(ln(3))-(2/(3)) - (ln(1)) ]
=[4 +(ln(2))- (1/(2)) ]-[3 +(ln(3))-(2/(3)) - (ln(1)) ]
=1+ln(2) - (1/(2))+(2/(3))-ln(3)+0
=(1/2 )+ (2/3)+ln(2)-ln(3)
=(7/6)+ln(2)-ln(3)
= (7/6)+ln(2/3)
is the solution :)

Who was saved from the traders?

It is Samson who is saved by Rosh’s band from the slave traders. Samson is one of the slaves in a pack train that is headed for Galilee, from Damascus. The train passes through the mountain where Rosh and his band of men live. It comprises of “two guards in the front and rear, four mangy camels, a string of mules, one litter with dinghy curtains, four tradesmen and the slaves.” Rosh is interested in Samson because he is the strongest of all the slaves. He is described as “towering” all the other slaves, “looking murderous” with “lash-ridged shoulders and an ugly scar.” After he is rescued from the slave traders, he is submitted to Daniel’s care. Daniel leads him to the cave where all the band members live, offers him supper and cuts lose his manacles. He thus learns to respect Daniel as his master.
Samson is rescued on the same day that Daniel meets his former schoolmate, Joel, who is accompanied by his sister Malthace. Daniel has been away from his village for about five years since he ran away from his master Amalek, who used to mistreat him. Therefore, Daniel is naturally happy to see Joel and his sister and talks to them a little about life in the village. He also develops a friendship with Joel and allows him to stay with him as they rescue Samson from the slave traders. Later Joel meets Rosh and tells him how much he would like to one day join his band so as to free Israel from the Romans.

In 1984 by George Orwell, what is the main conflict, and how do other conflicts help to illuminate the author’s message?

The main conflict in 1984 is between totalitarianism, represented by Big Brother, and autonomy, represented by Winston Smith. This conflict exists in the story as a man versus society conflict. Totalitarianism represents the utter obliteration of self in pursuit of an external idea. Big Brother explicitly tries to limit expressions of autonomy and feeling—for instance, by regulating language in a way that erases creative potential. Each time that Smith attempts to preserve his sense of self, he acts in a contradictory manner to these societal aims.
This conflict is also echoed in the children Winston hears playing. They have already learned the value of policing each other and of demanding full compliance with the unreachable demands of their totalitarian government. These children have taken the conflict Winston feels with society and been taught to have it directly with each other, as though they were all agents of the state. This represents a man versus man conflict.

I think using a Marxist lens would be helpful in this analysis in terms of locating the "main conflict" in this novel.
Just as Marxist literary approaches look at works of literature as projections of the social, cultural, and political period from which they originate, so too is George Orwell attempting to depict what happens in a society dominated by the rich.
The result of a burgeoning capitalist system is the production of a society based on the ongoing exploitation of the masses and lack of access to full economic and political equality of the prole (the worker, who is representative of the masses). 1984 is also a prime examination of the alienation that results within the economic schemes of capitalism. Orwell is interested in promoting critical consciousness of culture—a first step towards ‘liberating’ the reader. He is adept at illuminating the subtleties of consciousness at work in the dynamic between capitalist and prole.
In employing a Marxist lens for this novel, you may want to ask the following questions:
Are bourgeois values (competition, acquisitiveness, etc) compatible or incompatible with human happiness?
How are classes stratified/defined in this text? Does this text reflect an economic ideology?
What is the attitude toward labor furthered by this text?
https://literarydevices.net/1984-themes/

https://medium.com/@kelsilynelle/orwells-1984-from-theoretical-views-an-essay-638b5b1f8850

The central conflict of the novel 1984 is Man vs. Society, which is represented by Winston Smith vs. the Party (Big Brother). In the dystopian nation of Oceania, individualism is virtually extinct, and the Party controls every aspect of society. The citizens are under constant surveillance and suffer under the oppressive regime. Throughout the novel, Winston struggles to maintain his individuality under the watchful eye of Big Brother and even attempts to undermine the Party by joining the Brotherhood. Winston is completely opposed to every aspect of society and takes enormous risks, which eventually result in his arrest and torture.
One minor conflict that is presented throughout the novel and highlights the major conflict of Man vs. Society is Man vs. Self. In the novel, Winston struggles with the decision to remain alive in the dystopian nation or rebel against the Party. Winston fears being tortured and is fully aware that he is risking his life. However, Winston is inherently motivated to oppose Big Brother regardless of the consequences. Winston's desire to remain human and exercise independence conflicts with his will to survive. The conflict between Truth vs. Propaganda also emphasizes the central conflict of the novel. Mutability of the past and the overwhelming state-sanctioned propaganda disguise the truth, which makes Winston continually question his approach to rebelling against Big Brother. Winston desperately searches for concrete evidence to prove that life was better before the Revolution but cannot attain accurate historical records. Overall, the central conflict of the novel is Man vs. Society and the minor conflicts highlight Winston's struggles against Big Brother to warn readers about the dangers of totalitarianism.

How does the historical context of Salem Village and Hawth‘s own family inform the reading of the story?

Not unlike the Reverend Dimmesdale, Nathaniel Hawthorne was plagued by a shadow of guilt which darkened his life. Hawthorne's guilt found its source in his Puritanical ancestors, such as Judge Hathorne, who played a role in the condemning to death of people in the Salem Witch Trials of 1692. (Because of Judge Hathorne, Nathaniel changed the spelling of his surname.) The Scarlet Letter and other works of Hawthorne's reflect the sin-obsessed climate of the Puritan era. Hawthorne struggled to overcome the history of his family and some of the consequences of Puritanical attitudes about humankind and sin.
One of the attitudes that Hawthorne fought against was that of the Puritanical interpretation of a world in which sin has no place. Known for its intolerance of any spiritual weakness and a source of religious fanaticism, Puritanism made it nearly impossible to be holy. In his novel, Hawthorne demonstrates a repudiation of the concept of "an eye for an eye"; furthermore, he examines the psychological effects of sin on a person. Hawthorne desires communal values such as loving one another, suffering and rejoicing together, and, most of all "being true!" by being honest with oneself, and others and living as members of one body that recognizes that "to err is human" and all men are sinners. In contrast to Puritanism, Hawthorne, with his theme of The Individual vs. Society in The Scarlet Letter, offers through his main characters the concepts of people helping one another to communal values, to loving one another, to rejoicing and suffering together, and to living together as members of one body.