What important fact do we find out about the grandfather in the first three lines of the poem "Grandfather" by Oliver Shelley?

In the poem "Grandfather" by Oliver Shelley, the poet makes great use of visual imagery. The first three lines establish the relationship between the narrator and the subject. On line one, the narrator refers to the grandfather as "Our grandfather," showing that the narrator is directly related to the subject. The use of "our" also reveals that the narrator has a sibling or a cousin. The poet uses visual imagery to present the grandfather as sitting "by the sea" on "[h]is deck chair." The chair is atop a rug belonging, at least in part, to the speaker, as it is referred to as "our rug" which the grandfather's chair is settling into "the stones" by the sea.
Finally, and perhaps most importantly, the grandfather is revealed to be blind, which helps to explain why "his face takes sunlight like thirst." Throughout the remainder of the poem, the narrator shows that the grandfather absorbs and appreciates his experiences in ways that don't require sight. Somewhat ironically, Shelley does a great job of using visual imagery to show how one can appreciate the world without being able to see it.

What are the signs that Tom and Daisy have a bad marriage?

One of the first signs that Tom and Daisy have a bad marriage comes in chapter 1, when Nick visits Tom and Daisy for dinner. Daisy shows Nick her little finger, which is black and blue at the knuckle, and claims that Tom hurt it. The only way someone can cause another to bruise, especially the pinkie finger, is to grab the hand extremely hard. Tom never hurts Daisy physically through the rest of the novel, but he does not hesitate to break Myrtle's nose in chapter 2, so the audience can conclude that he is at least capable of such violence.
It is also in chapter 1 that the audience learns that Tom has a mistress, because she calls during dinner and he takes the call, in front of not only his wife but also Nick and Jordan Baker. Tom does not try to hide his mistress, and in chapter 2, he shows her off to Nick in New York.
Daisy is not shy about showing off her own affair with Gatsby in chapter 6, which causes Tom to investigate Gatsby and where he attained his wealth. But that affair is probably the only one Daisy has had up to this point in the story. Tom has had many affairs, even during his honeymoon with Daisy—in chapter 4, Nick recounts how Tom was in a car accident with a chambermaid as his passenger. In chapter 7, Daisy even mentions an affair in Chicago, which is why they left and moved to New York.
So, Tom and Daisy's marriage is bad from the beginning, and it never seems to improve through to the end of the novel. However, they are destined to stay together in misery.

What are the major stylistic and thematic differences between John Donne and John Dryden? 500 to 1000 words

Donne is, and has been since Samuel Johnson's evaluation of him in the 1770's, considered one of the "Metaphysical" poets. Like his contemporaries and successors Henry Vaughan, Andrew Marvell, and Abraham Cowley (and many others), Donne wrote a type of intellectual, subtle, and "difficult" verse, the most obvious feature of which is the use of "conceits." These are extended comparisons between unlike things in which Donne uses all his poetic power to show that the things being compared really are similar, though no one would have thought so to start out with. In "A Valediction: of Weeping" he begins

Let me pour forth
My tears before thy face, whilst I stay here,
For thy face coins them, and thy stamp they bear,
And by this mintage they are something worth,
For thus they be,
Pregnant of thee.

Here we have two striking metaphors probably no one but Donne would have thought of. A lover's tears, reflecting the image of his woman, are first likened to coins (and because they are coins, they have monetary value!), and then are likened to pregnant women. It could be incredible, but Donne presents it so lucidly and realistically that it makes perfect sense. This technique is used everywhere in his work. I would divide his poetic work into three categories: love poetry, satire, and devotional or religious verse. He frequently is concerned with sexuality and uses sexual imagery even in the religious poems, such as Holy Sonnet 14, "Batter my Heart, Three-Personed God." There is a tension everywhere in his work between sacred and profane and despite his piety, an impudent flouting of authority. He also has been considered by some critics such as C.S. Lewis to have had a rather derogating attitude to women, even by the standards of the early 1600's.
John Dryden was born in 1631, the year of Donne's death. By the time of Dryden's early adulthood England had gone through enormous turmoil with the Civil War, the Commonwealth, and the Restoration. Poetry changed enormously as well. Two minor poets of the mid 1600's, John Denham and Edmund Waller, have often been given credit for spearheading the use of the heroic couplet, rhymed iambic pentameter in which each couplet generally expresses a single thought or sometimes a tension between a duality within one thought. Dryden acknowledged the influence of these men and became the first great poet of the English neo-classical or "Augustan" age. Dryden's ideals were those of elegance of language and metrical form, proportion, balance, and a generally restrained manner of expressing emotion. All of these qualities are quite different from the hallmarks of Donne's poetry. Donne's use of conceits, by Dryden's time, was considered eccentric, and Donne's language and meter were considered lacking in smoothness or even "harsh," so that Dryden's successor Alexander Pope re-wrote two of Donne's Satires in order to "smooth out" the "rough numbers." In addition the similarly "rough" explicitness of Donne's love poetry was considered unrefined by Dryden's time.
Regarding content and theme, Dryden and Donne have more in common. Both men wrote satires concerning religion: Dryden's "The Hind and the Panther" is a satirical allegory In which animals represent the Roman Catholic and the Anglican Churches. But the age of the fervent devotional poetry of Donne and others was over by the late 1600's. England had been exhausted by religious warfare. After the Restoration, partly encouraged by the rather hedonistic Charles II, a somewhat more secular orientation began, though Dryden and other writers cointinued to express their Christian beliefs in a less personal way. Usually this was done in the form of satirical works such as the one mentioned above, and another of Dryden's, "Absalom and Achitophel." Increasing emphasis was placed on literary and political disputes in Dryden's work. His satiric poem "Mac Flecknoe" is an attack on his contemporary, the poet Thomas Shadwell. And, as a part of his (and others') finding inspiration and models in the poetry of antiquity, especially that of Emperor Augustus's period--hence the term Augustan--Dryden translated Virgil's Aeneid into English. This was then a model for Pope's similar translations of Homer several decades later. Both Dryden and Pope established the heroic-couplet form as a standard, making their era's poetry instantly recognisable to succeeding generations.
In summary, Donne's poetry deals with sex, religion, and satire in a highly intellectual form with complex metaphorical devices we call conceits. He uses a variety of metrical forms and styles. Fifty to 75 years later Dryden uses a more restrained, emotionally controlled, and formally uniform (the heroic couplet) style, focusing increasingly on satire and a self-conscious referencing of the poets of antiquity, especially those of the period of Augustus (27 BC- AD 14), such as Virgil and Horace.

How is the American man manipulative and selfish in "Hills Like White Elephants"?

In Hemingway's "Hills Like White Elephants," the American man is selfish because he has no interest in understanding the woman's point of view. The abortion probably needs to be discussed, and one could claim that by pointing out that the hills look like white elephants, the woman is just trying to avoid the subject, but the man's only objective is to persuade or manipulate her to go through with the operation.

"You've got to realize," he said, "that I don't want you to do it if you don't want to. I'm perfectly willing to go through with it if it means anything to you."
"Doesn't it mean anything to you? We could get long."
"Of course it does. But I don't want anybody but you. I don't want anybody else."

The woman has to make a show of anger before he finally admits his true feelings.

"Would you please please please please please please please stop talking?"
He did not say anything but looked at the bags against the wall of the station. There were labels on them from all the hotels where they had spent nights.
"But I don't want to," he said, "I don't care anything about it."

It is at this point the reader can fully understand the woman's point of view. She knows that the abortion will mean the end of their relationship and that she will probably have nowhere to go. From this short story, for example, the reader can see that the woman relies on the man to order the beer in Spanish and know that the train is coming in five minutes. How would she cope alone in what is apparently an alien culture?
From this perspective, the man's attempted manipulation of the woman is odious. He holds all the power in the relationship and can afford to think that only his opinion and view on life matters. It seems that as far as he and only he is concerned, one should always be in control of themselves. At the end of the story, he states that the other people "were all waiting reasonably for the train."

Much of “Hills Like White Elephants” consists of dialogue between the man and the woman. What makes this particularly remarkable is that the woman repeatedly insists that she does not want to talk to the man—she eventually goes so far as to ask him if he would “please please please please please please please stop talking?” But the man persists, ignoring her needs as he often does in the story.
Throughout the story, the man only has one objective, which is to persuade the woman to agree to an abortion (although this is never explicitly stated, it is strongly implied). When, in the opening moments of the story, she tries to discuss the scenery, he is withdrawn and refuses to engage. He ignores what is interesting to her and pushes the conversation to a topic that she does not want to discuss. What makes this behavior even more selfish and manipulative is that he first frames it around her desire and their wellbeing as a couple:

If you don't want to you don't have to. I wouldn't have you do it if you didn't want to. But I know it's perfectly simple.

Later, the man switches tactics, trying to draw sympathy as the victim of the situation, telling her that it will help him to stop worrying if she will follow through and have the procedure. His behavior focuses on his needs to the point where he ignores even her most basic request: for silence.

Why is Don Abbondio not celebrating the marriage of Lucia and Renzo?

As the local parish priest, Don Abbondio is naturally expected to preside at all church wedding ceremonies. The forthcoming betrothal of Renzo and Lucia is no exception; or at least, it shouldn't be. However, on the eve of the wedding, Don Abbondio is accosted in the street by a couple of thugs as he makes his way home. They tell him in no uncertain terms that he must not go ahead with the wedding ceremony; those are the express orders of Don Rodrigo, a powerful local baron.
Don Abbondio is, among other things, a complete physical coward, and so it doesn't take much persuasion from Don Rodrigo's goons to get him to call the wedding off. Indeed, he's so much of a coward that he can only bring himself to tell Renzo that the wedding has been postponed. But Renzo eventually gets the truth out of the hapless prelate. It turns out that Don Rodrigo wants Lucia for himself.

Single Variable Calculus, Chapter 3, Review Exercises, Section Review Exercises, Problem 72

The equation $x = \sqrt{b^2 + c^2 t^2}, t \geq 0$ represents a particle that moves along a horizontal line where $b$ and $c$ are positive constants.

a.) Determine the velocity and acceleration functions.


$
\begin{equation}
\begin{aligned}

\text{velocity } = \frac{dx}{dt} =& \frac{d}{dt} \sqrt{b^2 + c^2 t^2} = \frac{d}{dt} (b^2 + c^2t^2)^{\frac{1}{2}}
\\
\\
\frac{dx}{dt} =& \frac{1}{2} (b^2 + c^2 t^2)^{\frac{-1}{2}} \cdot c^2 (2t)
\\
\\
\frac{dx}{dt} =& \frac{\cancel{2} c^2 t}{\cancel{2} \sqrt{b^2 + c^2 t^2}}
\\
\\
\frac{dx}{dt} =& \frac{c^2 t}{\sqrt{b^2 + c^2 t^2}}
\\
\\
\text{acceleration } = \frac{d^2 x}{dt^2} =& \frac{d}{dt} \frac{c^2 t}{\sqrt{b^2 + c^2 t^2}}
\\
\\
\frac{d^2 x}{dt^2} =& \frac{\displaystyle \sqrt{b^2 + c^2 t^2} \cdot c^2 \frac{d}{dt} (t) - (c^2t) \cdot \frac{d}{dt} \sqrt{b^2 + c^2t^2}}{(\sqrt{b^2 + c^2t^2})^2}
\\
\\
\frac{d^2 x}{dt^2} =& \frac{\displaystyle \sqrt{b^2 + c^2t^2} \cdot c^2(1) - (c^2 t) \cdot \frac{\cancel{2} c^2 t}{\cancel{2} \sqrt{b^2 + c^2t^2}} }{b^2 + c^2 t^2}
\\
\\
\frac{d^2 x}{dt^2} =& c^2 \frac{\displaystyle \left[ \sqrt{b^2 + c^2 t^2} - \frac{c^2 t^2}{\sqrt{b^2 + c^2 t^2}} \right]}{b^2 c^2 t^2}
\\
\\
\frac{d^2 x}{dt^2} =& c^2 \frac{\displaystyle \frac{b^2 + c^2t^2 - c^2 t^2}{\sqrt{b^2 + c^2 t^2}}}{b^2 + c^2 t^2}
\\
\\
\frac{d^2 x}{dt^2} =& \frac{b^2 c^2}{(b^2 + c^2t^2)^{\frac{3}{2}}}


\end{aligned}
\end{equation}
$



b.) Show that the particle always moves in positive direction.

The particle is moving in a positive direction if $v(t) > 0$ that is $\displaystyle \frac{c^2 t}{\sqrt{b^2 + c^2 t^2}} > 0$. Sinc the denominator is always positive, recall that the square root function is defined only for positive solution. Therefore, the sign of the velocity function is affected only by the sign of the numerator. But we know that the function is defined only for $t \geq 0$ and we have $c$ as positive constant. Hence, $v(t)$ is always positive and the particle always moves in the positive direction.



$
\begin{equation}
\begin{aligned}


h'(x) =& \frac{1}{2} \left[ \frac{f9x)}{g(x)} \right] ^{\frac{-1}{2}} \cdot \left( \frac{g(x) f'(x) - f(x) g'(x)}{[g(x)]^2} \right]
\\
\\
h'(x) =& \frac{g(x) f'(x) - f(x) g'(x)}{\displaystyle 2 \sqrt{\frac{f(x)}{g(x)}} [g(x)]^2 }
\\
\\
h' =& \frac{gf' - fg'}{2 \sqrt{fg^3}}

\end{aligned}
\end{equation}
$

Calculus: Early Transcendentals, Chapter 6, 6.3, Section 6.3, Problem 34

y= x^3-x+1
y = -x^4+4x-1
The graph of the two equations are:

(Green curve graph of y=x^3-x+1 . Blue curve graph of y = -x^4+4x-1 .)
Base on the graph, the curve curves intersect at x~~0.421 and x~~1.23 .
To solve for the volume of the solid formed when the bounded region is rotated about the y-axis, apply method of cylinder. Its formula is:
V= int _a^b 2pi *r * h*dx
To determine the radius and height of the cylinder, refer to the figure below. Base on it, its radius and height are:
r = x
h = y_(upper) - y_(lower)
h=(-x^4+4x-1) - (x^3-x+1) = -x^4-x^3+5x - 2
Plugging them to the formula of volume yields:
V=int_0.42^1.23 2pi *x *(-x^4-x^3+5x-2)dx
V=2pi int_0.42^1.23 (-x^5-x^4+5x^2-2x)dx
V= 2pi (-x^6/6 - x^5/5+(5x^3)/3-x^2)|_0.42^1.23
V=2pi [ (-1.23^6/6-1.23^5/5+(5*1.23^3)/3-1.23^2)-(-0.42^6/6-0.42^5/5+(5*0.42^3)/3-0.42^2)]
V=2pi*0.5048
V=3.1717
Therefore, the volume of the solid formed is 3.1717 cubic units.