For what purpose alone was man sent into this life. What is this purpose? Discuss some means of fulfilling this purpose.

Tolstoy spent the last twenty years of his life, after his fame had been fully established, writing for the most part shorter works intended to convey a religious message. Some of the best known of these stories are "What Men Live By," "How much Land does a Man Need?," and "The Three Questions." The last of these deals with a king who seeks guidance from a hermit. Because the king ends up helping the hermit with his work in a field, the king escapes being killed by a man whose brother the king has executed. His good deed in aiding the hermit in his work has saved the king, and the moral of the story is that this is solely what man has been sent into the world for: to do good.
It is interesting that at the close of the 1968 film of War and Peace, the director Sergei Bondarchuk gives this moral to the character Pierre to speak. The story of War and Peace is so multifaceted that it cannot be interpreted as having a single "message." But at the time Tolstoy wrote the novel, he presumably had not yet experienced the religious epiphany that later motivated him to write the stark, simple parables such as "Three Questions." Throughout his whole life, however, Tolstoy seems to have been haunted by his somewhat wild and reckless youth, before he settled down and married. In some sense these late religious writings appear to be an attempt to atone for that past. Yet, as well-intentioned as those parables are, probably, as George Orwell wrote, no one today would be aware of Tolstoy's later writings had he not also been the author of War and Peace and Anna Karenina.

f(t) = arctan(sinht) Find the derivative of the function

f(t)=arctan(sinh(t))
Take note that the derivative formula of arctangent is
d/dx[arctan(u)]=1/(1+u^2)*(du)/dx
Applying this, the derivative of the function will be
f'(t) = d/(dt)[arctan(sinh(t))]
f'(t) = 1/(1+sinh^2(t)) *d/(dt)[sinh(t)]
Also, the derivative formula of hyperbolic sine is 
d/dx[sinh(u)]=cosh(u)*(du)/(dx)
Applying this, f'(t) will become
f'(t)= 1/(1+sinh^2(t)) *cosh(t)*d/(dt)(t)
f'(t)= 1/(1+sinh^2(t)) *cosh(t)*1
f'(t)= cosh(t)/(1+sinh^2(t))
f'(t)= cosh(t)/(cosh^2(t))
f'(t)= 1/cosh(t)  is the final derivative

What are some figurative devices in "The Ax-Helve" by Robert Frost?

In addition to those identified by the first educator, we can find still further figurative devices in Frost's "The Ax-Helve." Towards the end of the poem, for example, we see an example of allusion used as part of, and to illuminate, a simile. Allusion is valuable in poetry in that it offers us another context through which to understand the text: here, Baptiste stands the ax "erect, but not without its waves, as when / The snake stood up for evil in the Garden." This is an allusion to the serpent in the Garden of Eden as it is described in Genesis: the comparison invites us to consider the ax-helve as if it were a living thing, somewhat sinister, a thing standing upright which should not be in defense of something which should not be defended.
Baptiste's personification of the ax as "she" supports this idea that it has a life of its own in some way, and its own motivations. Earlier, when Baptiste is cutting the helve, he demonstrates that "its curves were no false curves / Put on it from without," again a suggestion that there is a certain power and certain attributes inherent to the ax-helve. The "long-drawn serpentine" of the speaker's machine-made ax-helve is contrasted, in its artificiality, to the helve which should stand like a snake almost under its own power, its natural strength already within and only needing to be coaxed out.

Robert Frost's poetry is known for being rife with figurative devices. In the poem, "The Ax-Helve," Frost makes use of many similes. A simile is a figurative device used to compare two things using "like" or "as."
"Of bending like a sword across the knee"
He also uses personification throughout the poem. Personification is giving human-like characteristics to something that is not human.
"And stood the axe there on it's horses hoof"
"And there it's strength lay"
Authors use figurative language for many reasons, but Frost uses figurative language to paint a picture in the reader's mind of what is going on and to emphasize certain emotions he is trying to portray throughout the poem. By the end of the poem, the reader has an image of exactly what has happened in the poem.

In this poem, a helve is the handle of a tool the narrator uses to chop wood. "The Ax-Helve," like all of Frost's poetry, is filled with literary devices. The most obvious comes in the form of similes, used to compare two things using "like" or "as." These lines describe how Baptiste, after taking the narrator's ax-helve, criticizes it and states how he prefers his helve:

"Like the two strokes across a dollar sign."
"He liked to have it slender as a whipstock."
"Of bending like a sword across the knee."

He also employs the use of personification to compare his helve to a woman, calling it "she" and pointing out how "she cocks her head."
Personification is used again when the narrator claims the alder branch is somehow holding him back from striking another alder branch.
Throughout the poem, Frost also uses alliteration as a sound device. Dialect is used to juxtapose our two characters. The way Baptiste speaks contrasts with the way the narrator speaks; Baptiste is French-Canadian, which is why he is speaking "French-English."

What problems did Washington have trouble with during his presidency?

Washington faced many struggles during his presidency, and his responses to them established enduring precedents. Let us look at a few major problems.
First, Washington had to deal with the fallout of the French Revolution, which broke out in 1789, just a few months after his inauguration. Americans generally supported the revolution in its early days, but after France went to war with the other monarchies in Europe, and the Revolution became more radical, it became a profoundly divisive and dangerous event. It took on special urgency when France and Great Britain went to war, because the United States had a treaty dating to the American Revolution with the French, who, through minister Edmond Genet, actively recruited Americans to join the war. Washington thought war against Britain would be ruinous to the new nation and issued a Proclamation of Neutrality in April of 1793. This set a precedent for American neutrality in European wars that endured until the First World War.
Another issue Washington faced was a fiscal crisis rooted in state and national debt. The American Revolution had been financed by debt in the form of foreign loans and bonds and cash issued by states. The bonds were nearly worthless, and American credit was virtually nonexistent when Washington took office. Alexander Hamilton, Washington's treasury secretary, devised a plan for addressing the nation's fiscal woes that included issuing federal bonds to redeem state debts, establishing an excise tax on whiskey, and chartering a national bank. Each of these steps was controversial, but the excise tax outraged western farmers, many of whom rose in rebellion in Pennsylvania.
These two problems contributed to the outbreak of partisan politics in the United States, a development not really anticipated in the structure of the Constitution. Two emerging factions began to coalesce around differing positions on domestic and foreign policy. One group, calling themselves Federalists, supported a robust national government and tended to favor Britain in the European war. The other, who became known as Republicans, supported limited federal government (with powers held by the states) and generally favored France. Partisan politics became increasingly vicious throughout Washington's presidency, giving him cause to warn against the "baneful effects of the spirit of party" in his Farewell Address.
https://millercenter.org/president/washington

Charles Darwin wrote a letter to a man pleading with him to read his book on evolution, but the man refused to do. A copy of the letter is on display at (I think) the Yorkshire museum. I have the names of John Phillips and Strata Smith. Who was it that the letter was written to, and is there a copy somewhere?

Do you mean Darwin's letters to fellow geologist John Phillips? These are stored in the geological collections of Oxford University Museum, but, thankfully, they have all been transcribed and are available online as part of a project by the Faculty of Geology.
Phillips was a contemporary of Darwin's and was from Yorkshire, which may be why you have in your mind that the letters are kept in a Yorkshire museum.
In this letter (https://www.darwinproject.ac.uk/letter/?docId=letters/DCP-LETT-2521.xml;query=;brand=default) Darwin tells Phillips that he will be sending him a copy of the Origin of Species and asks Phillips to please read the whole thing straight through--even though Darwin is fairly sure that Phillips will be "dead against it." He tells Phillips that he need not send any reply to the letter but asks him to please think before he starts to generate any "awful anathemas" against what Darwin has said.
We do not actually have the letter that Phillips wrote as a response, but Darwin later said that the response was "cautious but decidedly hostile."
You can see some other letters written by Darwin to Phillips here: https://www.darwinproject.ac.uk/search?search-correspondent="Phillips,%20John";f1-author=Darwin,%20C.%20R.
I think the first one linked is the one you are looking for, and Darwin's debate with Phillips is one of the most famous debates. Darwin later read Phillips's own book and noted that he was not surprised, but disappointed, to find that Phillips had rejected Darwin's conclusions.

"Golding illustrates that the source of human evil is fear." Provide evidence and quotations from for this thesis. I need 3 arguments and each argument requires 3 pieces of support. 2 of the pieces are direct quotations from the novel. The novel is Lord Of The Flies by William Golding.

That's a great thesis.  It makes a claim about the book that I feel can be strongly supported.  
There are plenty of instances in the book where Golding shows how the boys did something evil or acted in an evil manner because they are afraid of something.  More often than not, fear is what causes the boys to act.  Unfortunately, fear almost always causes the boys to act in hateful, malicious, and evil ways.  
Over the course of the entire novel, Golding shows readers a transformation that happens to the boys on the island.    When the boys are being introduced, readers might have high hopes for the overall survival of the boys.  They all seem to be friendly to each other, and they are actually excited by the possibility of being on the island together for a few days. Ralph actually announces to the boys that there is nothing to worry about.  In his opinion, the island is a place where they all can enjoy themselves until rescue shows up. 

“While we’re waiting we can have a good time on this island.”
He gesticulated widely.
“It’s like in a book.”
At once there was a clamor.
“Treasure Island–”
“Swallows and Amazons–”
“Coral Island–”

The allusion to The Coral Island is an interesting allusion because Golding was supposedly influenced to write Lord of the Flies because of his earlier experience with The Coral Island. He even borrowed character names from the book. In a nut shell, The Coral Island is about a group of boys that get stranded on an idyllic island paradise, and they successfully work together to build shelters and canoes. Additionally, they vanquish the island's "false gods" by using fire.  It's a story of bravery and goodness.  Golding's book is about fear and moral degeneration. 
Golding's book only initially begins like The Coral Island because the boys aren't afraid of anything.  The boys even hold an election in order to set up a basic government, a chain of command, and a division of labor.  

“Jack’s in charge of the choir. They can be—what do you want them to be?”
“Hunters.”
Jack and Ralph smiled at each other with shy liking. The rest began to talk eagerly.

After this moment, Ralph decides that the island needs some exploration.  He and two other boys excitedly head off, and everybody else (except Piggy) is content to hang out together.  
This entire fun vibe begins to fall apart in chapter 2 when the boys are given something to be fearful of and worry about.  One of the littluns tells the group that he saw a "beastie." 

Ralph laughed, and the other boys laughed with him. The small boy twisted further into himself.
"Tell us about the snake-thing."
"Now he says it was a beastie."
"Beastie?"
"A snake-thing. Ever so big. He saw it."
"Where?'
"In the woods."
[…]
"He says the beastie came in the dark."
[...]
There was no laughter at all now and more grave watching.

Immediately after this, readers are told that Jack "seized the conch."  He doesn't ask for it.  He takes it for himself and announces that he and his hunters would kill the beast if it existed.  In the previous chapter, Jack showed himself incapable of killing a pig that they might need for food; however, now that he is fearful, his inner bloodlust has been triggered.  
Over the course of the next few chapters, the boys' fear continues to escalate and grow.  Readers can see how it's becoming a problem for the group, and Ralph sees it too.  The littluns aren't sleeping because of their fear, and their talk of the beastie is beginning to put everyone else on edge.  Consequently, Ralph and Jack begin to argue and bicker with each other more than they actually work together. 
In an attempt to get everybody's fear under control,  Ralph calls another meeting.  He berates everybody for slacking off on their jobs.  His goal is to get everybody to focus on an assigned task.  If everybody is working on a task, there isn't time to always focus on fear. Ralph correctly realizes that all of the problems are linked to everybody's fear. 

“Things are breaking up. I don’t understand why. We began well; we were happy. And then—”
He moved the conch gently, looking beyond them at nothing, remembering the beastie, the snake, the fire, the talk of fear.
“Then people started getting frightened.”

Jack actually supports Ralph in this argument, but Jack is less tactful.  

“The thing is—fear can’t hurt you any more than a dream. There aren’t any beasts to be afraid of on this island.”

Jack also confidently tells everybody that he has been all over the island and hasn't seen any beast. 
Piggy also puts in his own opinion on the matter, and more or less says the same thing about not needing to fear anything. Unfortunately, he ruins his own advice by stating out loud that if the boys should fear anything it should be each other.

“Unless we get frightened of people.”

Fortunately, the pep talk seems to have worked.  Everybody is back to a bit of joking around until one of the littluns states something that nobody had thought of before.  

“He says the beast comes out of the sea.”

The meeting digresses into chaos, screaming, and insults.  

Jack was up too, unaccountably angry.
“Who cares what you believe—Fatty!”

Once again, fear has caused the boys to ignore all forms of decorum.  They are at each other's throats.  Jack goes running off, and many boys follow him.  It's the start of a serious division between Ralph's supporters and Jack's supporters.  
By chapter 8, fear and the fear of the beast has turned Jack, Roger, and the other choir boys into monsters.  They no longer hunt to supply everybody with food.  They hunt because they enjoy the kill, and they have even begun to mutilate carcasses by stabbing spears up an animal's anus. Additionally, fear causes Jack to begin making sacrificial offerings to the imagined beast. 

“This head is for the beast. It’s a gift.”

By the end of the story, whether or not Jack is afraid of the beast isn't clear.  What is clear though is that Jack is afraid of losing power to Ralph.  It's why Jack so badly wants Ralph dead. Jack has gotten a taste of real power, and he wants to keep it.  He's willing to be incredibly violent and cruel to keep it too.  That's how he keeps his power over the other boys as well.  They are afraid of Jack, and that fear motivates them to listen to his every command no matter how sinister.

“I said ‘grab them’!”
The painted group moved round Samneric nervously and unhandily. Once more the silvery laughter scattered. 

I'm unsure of what 3 specific arguments your essay is going to contain, but the above evidence and quotes can be tailored to help you with a variety of arguments.  

In “American History”, why is Elena so happy on the day of President Kennedy’s death?

In spite of the sadness that engulfs El Building and the surrounding environs on the day of President Kennedy’s death, Elena is happy because finally, Eugene has invited her over to his house. He wants the two of them to use the time to study for an American History test. The two also plan to walk together to the public library, later on. It appears that Elena is infatuated with Eugene. The story states that “there was only one source of beauty and light” for Elena that school year. That was “seeing Eugene” every opportunity she could. Elena says that “she had liked Eugene right away” because he spent most of his time reading at their kitchen table. She spends a lot of time watching his house from her bedroom window. In fact, she had liked him so much that she sought him out at school to introduce herself. Afterwards, the two of them walked home together most days.
However, Elena’s happiness on this particular day is short lived. When she gets to Eugene’s house, his mother sends her away, saying that Eugene certainly does not need her help in studying. She asks her to go back to her own house.