Summarize the major research findings of "Toward an experimental ecology of human development."

Based on findings of prior research, the author, Bronfenbrenner proposes that methods for natural observation research have been applied in a manner that fails to consider the changing environments that affect human behavior. Observation in one natural setting is not enough to fully understand human behavior. The examples the author offers relate to observation studies of child behavior and development. Bronfenbrenner suggests that researchers cannot fully understand child development within the context of a single setting, with a single set of adults.
The child may behave one way at home with both parents but display different behavior and react differently to each of his/her parents in a setting outside the home, such as at school, at a medical appointment, or in another setting outside the home. The author suggests that age, socioeconomic status, and other demographics may influence how the child responds to the father and to the mother. Bronfenbrenner gives an example of a child from a middle-class family, whose interactions favor the mother in a laboratory setting and the father in a home setting. At the same time, the child from a lower economic class tends to favor the father in the laboratory setting and the mother in the home setting. Therefore, unless the researcher is seeking to answer a single, specific question related to child development and the specific environment, a richer, more robust methodology is needed to make general observations related to child development and parent interactions across all settings. 
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.458.7039&rep=rep1&type=pdf

Single Variable Calculus, Chapter 3, 3.5, Section 3.5, Problem 79

Show that $\displaystyle a(t) = v(t) \frac{dV}{ds}$ of a particle that moves along a straight line with displacement $s(t)$, velocity $v(t)$ and the acceleration $a(t)$. Explain the difference between the meanings of the derivatives $\displaystyle \frac{dv}{dt}$ and $\displaystyle \frac{dv}{ds}$

Recall that $a(t) \displaystyle = \frac{dV}{dt}$ and $v(t) = \displaystyle \frac{ds}{dt}$


$
\begin{equation}
\begin{aligned}

a(t) =& \frac{dV}{dt} = \frac{dV}{ds} \left( \frac{ds}{dt} \right) = \frac{dV}{ds} v
\\
\\
& \text{So,}
\\
\\
a(t) =& v \frac{dV}{ds}
\\
\\


\end{aligned}
\end{equation}
$


$\displaystyle \frac{dV}{dt}$ represents how the velocity changes with respect to time. On the other hand, $\displaystyle \frac{dV}{ds}$ represents how the velocity changes with respect to displacement of a certain particle.

Does the quote "a plague on both your houses" have any significance in the play of Romeo and Juliet?

Mercutio utters this line -- "A plague o' both your houses!" -- after he has been killed by Tybalt.  Tybalt came looking for Romeo in order to challenge him to a fight because he was offended by Romeo's presence at the Capulets' big party the night before.  When Tybalt eventually finds Romeo, Romeo has just come from marrying Juliet -- Tybalt's cousin -- and so Romeo refuses to fight this man who he is now related to, by marriage.  Mercutio, not knowing this, interprets Romeo's refusal to fight as a "dishonorable, vile submission" (3.1.72), and he fights Tybalt on Romeo's behalf.  Romeo comes between them in a well-meaning but ill-advised attempt to stop the fight and promote peace, and Tybalt is able to stab Mercutio under Romeo's arm.  For several reasons, then, Mercutio feels that his death is actually the fault of both Romeo and Tybalt: as he lays dying, he curses both "houses," or families, for their roles in his death.  He curses each family to have some tragedy, and, obviously, both families do experience tragedy when their children -- Romeo and Juliet -- kill themselves rather than live without one another.

int_0^(1/2) arctan(x^2) dx Use a power series to approximate the value of the integral with an error of less than 0.0001.

 From a table of power series, recall that we have:
arctan(x) = sum_(n=0)^oo (-1)^n x^(2n+1)/(2n+1)
To apply this on the given problem, we replace the "x " with "x^2 ".
We get:
arctan(x^2) =sum_(n=0)^oo (-1)^n (x^2)^(2n+1)/(2n+1)
                        =sum_(n=0)^oo (-1)^n x^(2*(2n+1))/(2n+1)
                        =sum_(n=0)^oo (-1)^n x^(4n+2)/(2n+1)
                        = x^2 -x^6/3+x^10/5-x^14/7 +...
The integral becomes:
int_0^(1/2) arctan(x^2)dx = int_0^(1/2) [x^2 -x^6/3+x^10/5- ...]
To determine the indefinite integral, we integrate each term using Power Rule for integration: int x^n dx = x^(n+1)/(n+1) .     
int_0^(1/2) [x^2 -x^6/3+x^10/5-...]
=[x^3/3 -x^7/21+x^11/55-...]_0^(1/2)  
Applying definite integral: F(x)|_a^b = F(b)-F(a) .
F(1/2) or F(0.5)=0.5^3/3 -0.5^7/21+0.5^11/55- ...
                            = 0.0416667 - 0.0003720+0.0000089-...
F(0)=0^3/3 -0^7/21+0^11/55-...
          =0 -0+0 -...     All terms go to zero.
 We stop at the 3rd term since we only need error less than 0.0001 .
int_0^(1/2) arctan(x^2)dx =0.0416667 - 0.0003720+0.0000089
                                = 0.0413036
Thus, int_0^(1/2) arctan(x^2)dx~~0.0413 .

How is the neighborhood described?

The narrator of "Sonny's Blues" describes the neighborhood as "filled with a hidden menace which was its very breath of life." Though the place where he lives is a relatively new housing project, it has become, in his words, "already rundown." The playground is not populated in the daytime with children playing the innocent games of childhood; it is populated at night. Though Baldwin's narrator does not say what goes on there, readers understand that it is far from wholesome.
The narrator observes that the neighborhood where he lives as an adult is not much different from where he and Sonny grew up; it is, he says, as if "I was simply bringing him back into the danger he had almost died trying to escape." The streets of Harlem he describes are filled with subway stations, bars with jukeboxes spilling music into the streets, and neighborhood people gathering outside a barbecue joint to hold an impromptu street revival. The narrator remembers his and Sonny's mother telling their father they should try "to move to a neighborhood that might be safer for the children." He also remembers times when their apartment was filled with friends and neighbors on Sunday afternoons after big dinners when he felt safe and loved, but also aware of the dangers outside that lay waiting.

which process changes sedimentary rock into igneous rock

In the rock cycle, the thing that determines the type of a rock is the way the rock was formed. Igneous rocks are formed by the cooling and solidifying of molten rock (magma or lava), sedimentary rock is formed by deposition of sediments which are either compacted or cemented together, and metamorphic rock is formed when other rocks are subjected to extreme pressure and/or heat that is not enough to actually melt the rock. The heat and/or pressure can deform the rock and also cause different minerals to form, or else change the shape and distribution of existing minerals.
In the determination of whether a rock’s type is igneous, sedimentary, or metamorphic, it doesn’t matter what knd of rock it came from. It only matters how it was made. The rock in the question is igneous rock, so it had to solidify from molten rock. To become molten, the original sedimentary rock had to melt. Once molten, of course, the structure of the previously existing rock would disappear. The process that would transform a sedimentary rock, or any other rock, into an igneous rock, then, is melting or, to be more specific, melting followed by cooling and solidifying.

How is the following quote ironic, and what theme does it show? "We've got to have rules and obey them. After all, we're not savages."

In chapter 2, the boys fail to make a sustainable signal fire, and Ralph mentions that they need to put people in charge of maintaining the fire at all times. Ralph also says that they should have more rules and Jack agrees by saying,

"We've got to have rules and obey them. After all, we're not savages. We're English, and the English are best at everything." (Golding, 33)

Jack's comment is ironic because as the novel progresses, Jack and his band of hunters reveal their savage, primitive nature. Jack and his hunters paint their faces and become bloodthirsty barbarians as they hunt pigs, murder Simon and Piggy, and even attempt to kill Ralph.
After landing on the island, they rapidly descend into savagery and live like uncivilized beings. Jack's comment also emphasizes the theme of civility vs. savagery. As English schoolboys, Jack and the others have been taught that they are inherently civil and superior to other races, ethnicities, and cultures. However, Golding portrays all humans as inherently evil, wicked individuals without the restraints and influence of society to prevent them from acting like savages and indulging in their true desires.

Interpret the poem "Queen-Anne's-Lace."

The key device used by the poet in this poem is personification; he describes the flower Queen Anne's Lace as if it were a lover, combining the literal (the plant is powerful, "taking / the field by force; the grass / does not rise above it") with the figurative ("wherever / his hand has lain there is / a tiny purple blemish").
We may assume that the "he" in the poem represents the sun, driving the flowers to "blossom under his touch." As the sun and the Queen Anne's Lace are characterized as lovers, so the white spread of bloom across the field, the result of their growth together, is described as "desire," spreading in the form of blossoms. Like desire, too, the spread of blossom seems to reach a climax, after which the field is "empty," the flowers scattered as the "wish to whiteness" has gone over and the flowers have receded with the end of spring.

What two jobs does Jack claim for the choirboys?

In chapter one, "The Sound of the Shell," Jack and Ralph compete to be "chief" of the boys. When Ralph gets more votes than Jack does, Ralph graciously gives command of the choir to Jack. Jack says he wants them to be the island's hunters. After that, Jack leads the hunters as they stalk and eventually kill a pig.
In chapter two, "Fire on the Mountain," Ralph tells the other boys that his father is in the navy and has told him that the Queen has maps of the world, including the island on which they're stranded. He is convinced that a ship will come near and suggests that they maintain a signal fire on top of the highest hill. Jack volunteers his choir, the hunters, to be the ones who gather wood. Later, he declares that he will divide the choir into groups that will both maintain a lookout shift and keep the signal fire burning.

In chapter 1, the boys elect Ralph as chief, and he immediately tells Jack that the choir belongs to him. The first job that Jack claims for the choir is to be the group's hunters. Throughout the novel, Jack leads his choir on numerous hunting expeditions, where they brutally kill pigs and hold feasts. Jack and his hunters become bloodthirsty and are obsessed with hunting by the end of the novel. In chapter 2, Ralph holds an assembly and attempts to create a civil, organized society. The second job that Jack claims for his choir involves maintaining the signal fire. Jack volunteers his choir to watch over and feed the signal fire on the top of the mountain. Later on, Jack relieves his hunters from their duty of maintaining the signal fire and leads them on a hunting expedition. Unfortunately, a ship passes by the island, and the hunters are not on top of the mountain to fuel the signal fire, which leads to a heated argument between Ralph and Jack over duties and priorities.

How is the parent-child relationship shown through the novel Frankenstein by Mary Shelley?

A chief way Mary Shelley shows the parent-child relationship in Frankenstein is first through Victor's loving parents, who bestow affection and every kindness on him, feeling he was given to them by God. They therefore believe that they owe him a tender upbringing. As he recalls it:

Much as they were attached to each other, they seemed to draw inexhaustible stores of affection from a very mine of love to bestow them upon me. My mother’s tender caresses and my father’s smile of benevolent pleasure while regarding me are my first recollections. I was their plaything and their idol, and something better—their child, the innocent and helpless creature bestowed on them by heaven, whom to bring up to good, and whose future lot it was in their hands to direct to happiness or misery, according as they fulfilled their duties towards me.

Victor goes on to remember an idyllic childhood provided by his caring and gentle parents:

No human being could have passed a happier childhood than myself. My parents were possessed by the very spirit of kindness and indulgence. We felt that they were not the tyrants to rule our lot according to their caprice, but the agents and creators of all the many delights which we enjoyed.

Victor himself becomes a "parent" in a very different way, playing God and bringing a creature to life through assembling and animating dead body parts. The dysfunctional relationship of Victor to his creation could not be more different than Victor's loving relationship with his own parents. Victor is repulsed by his "child" and rejects it when it comes to life:

Breathless horror and disgust filled my heart. Unable to endure the aspect of the being I had created, I rushed out of the room. . . . A mummy again endued with animation could not be so hideous as that wretch.

When Victor next encounters his creation, he is again filled with horror and wants to kill it, knowing the creature has murdered his loved ones. The creature, however, pleads with Victor to be a loving father, telling Victor that he owes him kindness, for he is the one who gave him life:

Remember that I am thy creature; I ought to be thy Adam, but I am rather the fallen angel, whom thou drivest from joy for no misdeed. Everywhere I see bliss, from which I alone am irrevocably excluded. I was benevolent and good; misery made me a fiend. Make me happy, and I shall again be virtuous.

The creature, feared and hated by everyone, recognizes that loving parenting will bring out his benevolent side and make him good. On the inside, Frankenstein's creation desires to be a caring member of society. It is simply his outward shell that is hideous. He only becomes a murderer because everyone has rejected him: the love he tried to show was met with fear, hatred, and disgust.
Nevertheless, Victor is unable to get past the creature's outer appearance and, now, the havoc the creature has brought to Victor's family through acting out his rage and grief in murder. Victor is never able to transcend his repulsion toward his "child." He is never able, ironically, to replicate the loving and caring behavior he most appreciated from his own parents.
Shelley is critiquing playing God, but she is also suggesting that having played God, Victor is responsible for the outcome of his actions and should have treated his creation as a decent parent would.

What is the theme of the play The Admirable Crichton?

The major theme in the play is social class and how it's determined in and out of English society.
Social class and the various ways it's maintained, as well as its effects on people, is an important factor in the story. When a group of English aristocrats and their servants are marooned on an island, none of the pampered people know how to care for themselves. Though they try to conform to English standards at first, the only person who is able to thrive in the environment is the butler Crichton. He quickly becomes the leader of the group and this is affirmed several times despite power struggles from Lord Loam and the other aristocrats. When they're rescued and return to traditional society, however, everyone reassumes their normal place. Only Lady Mary says that perhaps England itself is wrong for the way it puts people in social classes; Crichton is a product of English society, though, and disagrees with her. He says, "My lady, not even from you can I listen to a word against England."

One of the most abiding themes of the play is the fluidity of social class, and especially how easily it can change under certain environmental conditions. Crichton, a humble butler, becomes the dominant character on the desert island, due to his intelligence and resourcefulness. In the so-called civilized world, Crichton would never get the opportunity to show his true character. But here on a desert island he flourishes among the hapless aristocrats who are supposedly his social superiors.
Social class is presented in the play as being highly artificial, a product of an equally artificial society. It says something about the rigidities of class structure in Edwardian England that someone from a relatively humble background can only really achieve a position of authority on a remote desert island, far away from his native shores. There is a natural aristocracy in this world, it would seem, and Crichton is a part of it, but only—appropriately enough—in the natural world.

College Algebra, Chapter 9, 9.1, Section 9.1, Problem 70

Define the sequence
$\displaystyle G_n = \frac{1}{\sqrt{5}} \left( \frac{(1+\sqrt{5})^n - (1-\sqrt{5})^n}{2^n} \right)$
Find the first 10 terms of this sequence using a calculator. Compare to the Fibonacci Sequence $F_n$

$
\begin{equation}
\begin{aligned}
G_ 1 = \frac{1}{\sqrt{5}} \left( \frac{(1 + \sqrt{5})^1 - (1 - \sqrt{5})^1}{2^1} \right) = 1\\
\\
G_ 2 = \frac{1}{\sqrt{5}} \left( \frac{(1 + \sqrt{5})^2 - (1 - \sqrt{5})^2}{2^2} \right) = 1\\
\\
G_ 3 = \frac{1}{\sqrt{5}} \left( \frac{(1 + \sqrt{5})^3 - (1 - \sqrt{5})^3}{2^3} \right) = 2\\
\\
G_ 4 = \frac{1}{\sqrt{5}} \left( \frac{(1 + \sqrt{5})^4 - (1 - \sqrt{5})^4}{2^4} \right) = 3\\
\\
G_ 5 = \frac{1}{\sqrt{5}} \left( \frac{(1 + \sqrt{5})^5 - (1 - \sqrt{5})^5}{2^5} \right) = 5\\
\\
G_ 6 = \frac{1}{\sqrt{5}} \left( \frac{(1 + \sqrt{5})^6 - (1 - \sqrt{5})^6}{2^6} \right) = 8\\
\\
G_ 7 = \frac{1}{\sqrt{5}} \left( \frac{(1 + \sqrt{5})^7 - (1 - \sqrt{5})^7}{2^7} \right) = 13\\
\\
G_ 8 = \frac{1}{\sqrt{5}} \left( \frac{(1 + \sqrt{5})^8 - (1 - \sqrt{5})^8}{2^8} \right) = 21\\
\\
G_ 9 = \frac{1}{\sqrt{5}} \left( \frac{(1 + \sqrt{5})^9 - (1 - \sqrt{5})^9}{2^9} \right) = 34\\
\\
G_{10} = \frac{1}{\sqrt{5}} \left( \frac{(1 + \sqrt{5})^{10} - (1 - \sqrt{5})^{10}}{2^{10}} \right) = 55\\
\end{aligned}
\end{equation}
$

Using Fibonacci Sequence $F_n = F_{n-1} + F_{n -2}$
Since $F_1 = 1$ and $F_2 = 2$, then

$
\begin{equation}
\begin{aligned}
F_3 &= F_2 + F_1 = 1 + 1 = 2 &&& F_7 &= F_6 + F_5 = 8 + 5 = 13\\
\\
F_4 &= F_3 + F_2 = 2 + 1 = 3 &&& F_8 &= F_7 + F_6 = 13 + 8 = 21\\
\\
F_5 &= F_4 + F_3 = 3 + 2 = 5 &&& F_9 &= F_8 + F_7 = 21 + 13 = 34\\
\\
F_6 &= F_5 + F_4 = 5 + 3 = 8 &&& F_{10} &= F_9 + F_8 = 34 + 21 = 55
\end{aligned}
\end{equation}
$

Calculus of a Single Variable, Chapter 7, 7.4, Section 7.4, Problem 7

Arc length (L) of the function y=f(x) on the interval [a,b] is given by the formula,
L=int_a^bsqrt(1+(dy/dx)^2) dx, if y=f(x) and a <= x <= b,
Now let's differentiate the function,
y=3/2x^(2/3)
dy/dx=3/2(2/3)x^(2/3-1)
dy/dx=1/x^(1/3)
Now let's plug the derivative in the arc length formula,
L=int_1^8sqrt(1+(1/x^(1/3))^2)dx
L=int_1^8sqrt(1+1/x^(2/3))dx
L=int_1^8sqrt((x^(2/3)+1)/x^(2/3))dx
L=int_1^8(1/x^(1/3))sqrt(x^(2/3)+1)dx
Now let's evaluate first the indefinite integral by using integral substitution,
Let t=x^(2/3)+1
dt=2/3x^(2/3-1)dx
dt/dx=2/(3x^(1/3))
dx/x^(1/3)=3/2dt
intsqrt(x^(2/3)+1)(1/x^(1/3))dx=int3/2sqrt(t)dt
=3/2(t^(1/2+1)/(1/2+1))
=3/2(t^(3/2)/(3/2))
=t^(3/2)
=(x^(2/3)+1)^(3/2)
L=[(x^(2/3)+1)^(3/2)]_1^8
L=[(8^(2/3)+1)^(3/2)]-[(1^(2/3)+1)^(3/2)]
L=[5^(3/2)]-[2^(3/2)]
L=11.18033989-2.828427125
L=8.351912763
Arc length (L) of the function over the given interval is ~~8.352

Precalculus, Chapter 9, 9.4, Section 9.4, Problem 72

You need to remember what a quadratic model is, such that:
a_n = f(n) = a*n^2 + b*n + c
The problem provides the following information, such that:
a_0 = 3 => f(0) = a*0^2 + b*0 + c => c = 3
a_2 = 0 => f(2) = a*2^2 + b*2 + c => 4a + 2b + c = 0
a_6 = 36 => f(6) = a*6^2 + b*6 + c => 36a + 6b + c = 36
You need to replace 3 for c in the next two equations, such that:
4a + 2b + 3 = 0 => 4a + 2b = -3
36a + 6b + 3 = 36 => 36a + 6b = 33 => 18a + 2b = 11
Subtract the equation 4a + 2b = -3 from the equation 18a + 2b = 11 :
18a + 2b - 4a - 2b = 11 + 3
14a = 14 => a = 1
Replace 1 for a in equation 4a + 2b = -3 , such that:
4 + 2b = -3 => 2b = -7 => b = -7/2
Hence, the quadratic model for the given sequence is a_n = n^2 - (7/2)*n + 3.

Why does Angela search under the hoods of the cars in chapter 14?

In chapter 14 of The Westing Game, Angela checks under the hood of the cars because she and Sydelle believe there may be more clues under one of them. In chapter 8, Angela and Sydelle receive the following clues: good, hood, from, spacious, grace. Sydelle reads these as one sentence: “Good gracious from hood space.” She says that as soon as the parking lot is cleared, they can search the hoods of the cars. She suggests that maybe they’ll find more clues or a map or the murder weapon. After Sydelle is injured in the restaurant bomb at the end of chapter 13, Angela takes it upon herself to search the parking lot. She disguises herself in her mother’s old beaver coat and hat and Turtle’s red boots and searches each car in the parking lot, but she doesn’t find anything.

In chapter 14 of The Westing Game, the teams are actively working on sets of clues in order to solve the mystery and win the game. Per Sydelle's instructions, Angela searches under the hood of each car in the parking lot of Sunset Towers, with the goal of either finding another clue or in some way getting closer to making sense of their clues. The words Sydelle and Angela have gathered so far are GOOD, HOOD, FROM, SPACIOUS, GRACE, KING, QUEEN, PURPLE, WAVES, ON(NO), GRAINS, and MT. In an attempt to make sense of the seemingly unrelated string of words, Sydelle repeatedly puzzles over and rearranges them, resulting in the phrase "good gracious from hood space," the answer to which she suspects may be found in the parking lot. Since Angela finds nothing of interest when searching the cars, we can conclude that this particular mission was unsuccessful.

Who was Herodotus?

Herodotus was an ancient Greek historian, known as "the father of history" due to his innovations in historiography, or the study of history. Prior to Herodotus, history as a formal academic discipline didn't really exist. Past events tended to be jumbled up with myth, fable, and legend, so much so that it was difficult to establish what had really happened in history.
Herodotus adopted a completely new method for studying history, as can be seen in his monumental account of the Persian Wars. Known simply as The Histories, they set out to provide an exhaustive account of what really happened during this epic conflict. Previously, historical accounts tended to be fragmentary, little more than disjointed bits of travelogue. Herodotus was the first to recognize the importance of combining all the various pieces of information concerning a historical event into a coherent narrative that would enable the reader to gain a broader perspective on things.
However, Herodotus's encyclopedic approach to writing history has been criticized for insufficient academic rigor. There's very little in the way of analysis in Herodotus's work; he presents all the elements of his story as if they were of equal importance. Furthermore, Herodotus did not entirely dispense with myth and fable; they are still present in his narrative, though they are generally much easier to discern than in previous chronicles. For the most part, Herodotus used fictitious elements to serve the needs of the narrative, to make it flow more naturally and more entertaining to read.
Whatever his shortcomings as a historian, Herodotus put the academic study of history on a firm footing. To a large extent, historians ever since have been building upon foundations that he first established.

What is a brief account of the packing incident in Three Men in a Boat by Jerome K. Jerome?

The "packing incident" can be found in chapter 4. It's another great sequence that continues to show that J., Harris, and George are complete, bumbling idiots that don't know it. The incident begins with the men having gathered all of their stuff together that needs to be packed. J. volunteers to do the packing, and the other two men sit back to watch. This bugs J. because what he intended was to volunteer to tell the other guys what needed to be packed when and where.

This was hardly what I intended. What I had meant, of course, was, that I should boss the job, and that Harris and George should potter about under my directions, I pushing them aside every now and then with, “Oh, you—!” “Here, let me do it.” “There you are, simple enough!”—really teaching them, as you might say.

J. eventually gets the bag all packed, and then Harris mentions that the boots didn't get packed. J. then has to unpack some stuff, pack the boots, and repack the stuff. He then can't remember if he packed his toothbrush or not, so he proceeds to unpack everything in order to find it. He finds the toothbrush and repacks everything only to have George ask about the soap being packed. J. has had enough by this point and says that he doesn't care about the soap.
Next, George and Harris make an attempt to pack the food and dishes. It's a hilarious sequence in which dishes are broken, jars of food are smashed, and butter is smeared everywhere.

They upset salt over everything, and as for the butter! I never saw two men do more with one-and-twopence worth of butter in my whole life than they did. After George had got it off his slipper, they tried to put it in the kettle. It wouldn’t go in, and what was in wouldn’t come out. They did scrape it out at last, and put it down on a chair, and Harris sat on it, and it stuck to him, and they went looking for it all over the room.

Which is more important to Sophocles, family or authority? Look at Antigone, Ismene, Creon, and Haimon and at what happens to them and their relationships. Cite specific quotes from the play to support each claim.

Antigone comes from a seriously dysfunctional family. Antigone's father, Oedipus, former King of Thebes, killed his father, Laius, who was King of Thebes before Oedipus. Oedipus didn't know that Laius was his father when he killed him, but the fact remains that Oedipus killed his own father.
Antigone's mother, Jocasta, is also Oedipus's mother. Antigone is therefore her father's sister. Oedipus didn't know that Jocasta was his mother when he married her and had children with her, but the fact remains that Oedipus married his own mother.
When it was discovered in Oedipus Rex that Oedipus had married his own mother, Jocasta, his wife/mother, took her own life. Oedipus then poked out his own eyes when he discovered Jocasta's body and exiled himself from Thebes.
Antigone has a younger sister, Ismene, who is afraid of her own shadow. Antigone also has (had) two brothers, Polyneices and Eteocles, who killed each other in a civil war over the throne of Thebes, which is where the story of Antigone begins.
Creon, Antigone's uncle and brother of Jocasta, is now King of Thebes. Compared to Antigone's side of the family, Creon and his family seems almost normal. According to legend, Creon and his wife, Eurydice, had seven children, although only one son, Haemon, appears in Antigone. Haemon is betrothed to Antigone, which, if Antigone's family history is any indication, does not bode well for Haemon.
Antigone loves her family. She complains about them and about the problems of being Oedipus's daughter (and sister), but she loves them nonetheless and says,

Ismene, sister of my blood and heart,See'st thou how Zeus would in our lives fulfillThe weird of Oedipus, a world of woes!For what of pain, affliction, outrage, shame,Is lacking in our fortunes, thine and mine?

Antigone tells Ismene about Creon's edict that Eteocles is to be given a state funeral and a hero's burial since he fought on the side of Thebes, but Polyneices is to be left unburied in the desert. Anyone who defies Creon's edict will be punished by death.
Antigone puts it to Ismene directly:

So stands it with us; now 'tis thine to showIf thou art worthy of thy blood or base.

Antigone is asking Ismene if, in spite of all the hardship that the family has endured, Ismene is worthy of being considered a member of their family and doing what's right by helping Antigone bury Polyneices.
Ismene avoids answering the question and asks Antigone why she intends to bury Polyneices in spite of Creon's edict. Antigone answers,

My brother, and, though thou deny him, thine.No man shall say that I betrayed a brother.

There it is. This is how Antigone feels about family in general, and her brother in particular.
Ismene keeps pressing the point, hoping that Antigone will change her mind. Antigone replies,

What right has he to keep me from my own?

This discussion is going nowhere. Disgusted with Ismene's cowardice, Antigone leaves her to go bury Polyneices by herself.
Unlike Antigone, Creon believes wholeheartedly in the authority of the state and his own authority as King:

Now that his two sons perished in one day,Brother by brother murderously slain,By right of kinship to the Princes dead,I claim and hold the throne and sovereignty.Yet 'tis no easy matter to discern... if one who reigns supremeSwerve from the highest policy, tongue-tiedBy fear of consequence, that man I hold,And ever held, the basest of the base.And I contemn the man who sets his friendBefore his country. For myself, I callTo witness Zeus, whose eyes are everywhere,If I perceive some mischievous designTo sap the State, I will not hold my tongue;Nor would I reckon as my private friendA public foe, well knowing that the StateIs the good ship that holds our fortunes all:Farewell to friendship, if she suffers wreck.Such is the policy by which I seekTo serve the Commons ...

Creon sets a very high standard for himself, and it remains to be seen whether he can meet that standard.
Creon's son, Haemon, does his best to speak on Antigone's behalf, while at the same time trying not to antagonize Creon. Creon repeatedly falls back on his position in the state, and as the state, to justify his edict and his death sentence against Antigone.

CREON. ... But he who overbears the laws, or thinksTo overrule his rulers, such as oneI never will allow. Whome'er the StateAppoints must be obeyed in everything,But small and great, just and unjust alike. ...
Is not this maid an arrant law-breaker?
HAEMON. The Theban commons with one voice say, No.
CREON. What, shall the mob dictate my policy?
... Am I to rule for others, or myself?
HAEMON. A State for one man is no State at all.
CREON. The State is his who rules it, so 'tis held.

The Chorus calls Antigone to task for defying Creon's edict and putting her own feelings and beliefs above the state:

Religion has her chains, 'tis true,Let rite be paid when rites are due.Yet is it ill to disobeyThe powers who hold by might the sway.Thou hast withstood authority,A self-willed rebel, thou must die.

Teiresias, the blind seer-prophet, appears to tell Creon that the gods are offended by his actions and hold Creon accountable for the unrest caused by his edict and by his decision to condemn Antigone to death:

O King, thy willful temper ails the State,For all our shrines and altars are profanedBy what has filled the maw of dogs and crows,The flesh of Oedipus' unburied son.Therefore the angry gods abominateOur litanies and our burnt offerings...

Teiresias prophesizes dire consequences if Creon goes through with Antigone's execution.

Know then for sure, the coursers of the sunNot many times shall run their race, beforeThou shalt have given the fruit of thine own loinsIn quittance of thy murder, life for life;For that thou hast entombed a living soul,And sent below a denizen of earth,And wronged the nether gods by leaving hereA corpse unlaved, unwept, unsepulchered.Herein thou hast no part, nor e'en the godsIn heaven; and thou usurp'st a power not thine.

The Chorus joins in against Creon.

CHORUS. Son of Menoeceus, list to good advice. ...
Go, free the maiden from her rocky cell;And for the unburied outlaw build a tomb.
CREON. Is that your counsel? You would have me yield?
CHORUS.Yea, king, this instant. Vengeance of the godsIs swift to overtake the impenitent.

Creon hurries to the cave where Antigone has been closed up, but he arrives too late. Antigone has already taken her own life. Haemon is there, too, and he first tries to kill Creon, and failing that, he kills himself. When Eurydice hears about Haemon's death, she kills herself as well.
Creon's blind adherence to the rules of the state—his rules—leads to the death of three members of his family, and benefits the state in no way whatsoever.
Is the family more important to Sophocles than the state? Although it appears that Sophocles has constructed the play to clearly champion the family, he also warns of the damage that can be done to the state and to the family by a family member who fails to respect and conform to the laws of the state.
Are the conflicts that arise in Antigone between the family and the state caused by Antigone putting the family before the state, or by Creon putting the state before the family? Is it Creon's edict that results in the deaths of Antigone, Haemon, and Eurydice, or is it Antigone's defiance of Creon's edict that results in their deaths?

While both family and authority are important to Sophocles, the importance of honoring family seems a bit more important to him when the fates of Antigone and her family are considered. Creon's realization that he caused the tragedy in the story by defying the gods implies that honoring family is the will of the gods—because the gods were displeased when he chose to honor the laws of the land as the King of Thebes.
Antigone chooses to bury her brother, whom her Uncle Creon, the new King of Thebes, ordered to be left unburied and unsanctified as punishment for warring against his brother. She doesn't deny her crime and accepts her death sentence when it is handed down. In the end, she kills herself before the death sentence is rescinded. Antigone values family over authority, saying:

I urge no more; nay, wert thou willing still,I would not welcome such a fellowship.Go thine own way; myself will bury him.How sweet to die in such employ, to rest,--Sister and brother linked in love's embrace--A sinless sinner, banned awhile on earth,But by the dead commended; and with themI shall abide for ever. As for thee,Scorn, if thou wilt, the eternal laws of Heaven.

To Antigone, honoring her family is also honoring the gods.
Ismene refuses to help Antigone bury Polyneices. She says it's not possible to do so, because his corpse is being guarded. When Antigone is caught, Ismene falsely confesses —but Antigone defends her. Nevertheless, Ismene is imprisoned by Creon and later released before Antigone's death. Ismene chooses to obey the law and preaches the same to Antigone, saying:

Shall we not perish wretchedest of all,If in defiance of the law we crossA monarch's will?—weak women, think of that,Not framed by nature to contend with men.Remember this too that the stronger rules;We must obey his orders, these or worse.

Ismene survives the play, but many of the people she loves are dead. 
Haemon, Creon's son and Antigone's fiance, appears to support his father but subtly tries to convince him to spare Antigone, claiming the city is on her side. He tries to appeal to Creon, saying that Creon isn't considering true justice and is immature in thought. Haemon insists: "A State for one man is no State at all. As Monarch of the desert thou wouldst shine," telling his father that his thoughts are flawed. They exchange harsh words, and Haemon swears he'll never speak to Creon again as he leaves. After Antigone is found dead, Haemon attempts to kill his father and then kills himself.
Creon orders Antigone to be put to death for burying Polyneices in defiance of his order. Though he spares Ismene, he has Antigone sealed in a cave. When a blind prophet warns him the gods are displeased with his treatment of Polyneices and Antigone, he sends men to free her—only to find that she's dead. He loses his son and wife to suicide and blames himself for what has happened, saying:

Lead me away. I have been rash and foolish.I have killed my son and my wife. I look for comfort; my comfort lies here dead. Whatever my hands have touched has come to nothing. Fate has brought all my pride to a thought of dust . . .

In the end, Sophocles respects both family and authority but considers honoring family to be the will of the gods, which must be respected.

How do you view the character Lily in The House of Mirth by Edith Wharton?

Edith Wharton's The House of Mirth presents Lily as an extremely shallow character who desperately wants to elevate her social status through a suitable marriage. For this reason, she refuses to wed Seldon, who is her closest friend and confidante. Her inability to control the wealth she does have eventually causes her financial ruin, and her family wants nothing to do with her when rumors begin. This would imply that Lily is indeed selfish and materialistic.
However, smaller plot details shade Lily's character in a different way. Twice she denies courses of action which would solve her financial difficulties because they would contradict her ethical values, first by denying the married Mr. Gus Trenor's attempts at wooing her, and then refusing to blackmail Mrs. Bertha Dorset (the woman spreading rumors about Lily) when she uncovers another affair.
Lily is a romantic at heart, and though she desires money and social status, she also wants real love in her marriage. Failing to find this, she commits suicide at the end of the novel.
Lily is not a flat character with only shallow and materialistic qualities, but rather a well-rounded tragic heroine who cannot achieve her dreams without sacrificing her sense of self, and ends up recognizing the impossibility of her goals and refusing to go on any longer.

What is the irony of the gifts that Jim and Della exchanged?

Irony is when events turn out the opposite of what is planned. In this story, newlyweds Della and Jim plan an amazing Christmas gift for each other. Both also make a big sacrifice to get the gift they think will bring joy to the other person.
Della sells her beautiful, beloved hair, that falls past her knees, to get money for Jim's gift. She uses the money to buy Jim an expensive watch chain for his beloved watch.
Jim sells his cherished watch to buy an expensive comb and brush set for Della's beautiful hair.
The irony is that both gifts are useless to the recipient. Both Jim and Della sold what made the gift precious: Della has little hair left to brush, and Jim has no watch left to attach his watch chain to.
Nevertheless, each one demonstrated love for the other, and this, O'Henry says, is the most important gift of all.

The irony regarding Jim's and Della's Christmas gifts to each other arises from the fact that neither individual can use their significant other's specific gift. Jim ends up selling his expensive watch in order to buy Della a pair of precious combs for her beautiful hair, while Della sells her long hair to purchase Jim a watch fob for his prize timepiece. Ironically, each person has sold their most prized possession in order to pay for an expensive gift that compliments their special personal belonging. Jim is the first to recognize the situational irony when he enters his home and sees that Della has cut all of her hair off. Jim stands with a "strange expression" on his face while Della attempts to explain that she sold her precious hair. After Della opens Jim's gift and discovers that he bought her an expensive set of combs, Della tells Jim that she wishes to see his watch and realizes that he no longer has it. Ironically, each person's gift is useless, but their love for each other is evident, and they appreciate each other's personal sacrifice.