How was the transformation of classes into masses possible?

In Arendt's The Origin of Totalitarianism, the grouping of people can seamlessly transition from a "class" structure to a "mass of humanity." Classes, she explains, are the natural social divisions that are inherently present in large groups of people. Because of their similarities, people of a certain class feel a sense of unity and even pride of being in a certain class.
Over time, however, especially in the more recent industrial ages, these classes begin to break down. The community bonds are harder to forge because of the larger size of societies, and individuals act in their own best interests more than in the interests of society or the class at large. In the presence of a totalitarian leader, such as Hitler or Mussolini, this mass of individuals can easily be swayed and influenced, as they are all concerned with self-preservation and self-interest. They will act as a group to save themselves—for instance, people in Nazi Germany were quick to distance themselves from Jewish individuals. Even though they are acting as individuals, they are doing so as a whole population, and a dictator can use this to their advantage to leverage a society for their personal gain. In this way, the classes can become the masses.

According to Arendt in The Origins of Totalitarianism, people in modern society become alienated from each other. They experience anomie, which is the breakdown of traditional social bonds and traditional morality. People begin to freely float as random individuals rather than experience themselves primarily as members of a group. This makes the transformation from class to mass possible.
Arendt calls the traditional groups people once identified with "classes." Classes had a strong sense of collective identity, with shared moral values. They also had a shared sense of purpose.
When totalitarian dictators come along, they exploit anomie. They pull together a large number of disparate individuals, which Arendt calls a mass rather than a class. Theses masses are easily manipulated because they don't have a strong sense of group identity. What the mass desires most of all is a sense of belonging and faith that a strong leader is in charge. A mass isn't that concerned with the content of what they are asked to believe in. The dictator is thus able to mold the mass any way he wants. Arendt argues that the shallowness of conviction in a mass movement is why so many Germans were able to abandon Nazism rapidly and completely after the war.

Frankenstein deserts his creation after putting in countless hours and energy into it, why?

In many ways, Victor Frankenstein is more an artist than a scientist, thus making the Creature more of a "masterpiece" than an "experiment". Victor's interest is in the act of creating and in accomplishing something seemingly impossible. Though he envisions a new species heralding him as its creator, he doesn't actually consider the practical implications of creating life or the responsibility he will have to that life.
Additionally, Victor is unusually concerned with appearance. The relative pleasantness or unpleasantness of a person's physical appearance dictates much of how Victor feels about that person. Notice the difference in his descriptions of M. Krempe and M. Waldman.
Therefore, when faced with a "masterpiece" which is ugly instead of beautiful; a living person rather than a work of art (and a hideous one, at that, which in his mind equals evil) he abandons it.

Victor Frankenstein deserts his creature after having put years of effort into making him because, in the moment that the creature comes to life, "the beauty of the dream vanished, and breathless horror and disgust filled [his] heart."  His dream of creating life, like a god, resulted in a terrifyingly ugly being, even though he had chosen the creature's features to be beautiful.  He describes the creature as "hideous" and he runs away from it, out into the night.  Victor feels horror, simple horror, and so he does what most human beings do when they are terribly scared, and that is run.  Disappointment also plays a large role in Victor's reaction to and desertion of his creature.  He had hoped for glory and gratitude from a new race of beings, and, instead, his creation is so horrible to look upon that even he, its maker, cannot do it. 

What is the comical element in The Tempest?

In broadest terms, literature falls into two categories: comedy or tragedy. Comedy has a happy ending, whereas tragedy has a sad ending, usually through the deaths of one or more main characters.
Therefore, the first comic element in The Tempest is its happy ending. Not only doesn't anyone die, Prospero, influenced by the sprite Ariel, decides to behave mercifully and forgive those who wronged him, even if they don't deserve it.
In between the beginning and the end, however, are a number of comic scenes. Shakespeare usually uses lower class characters to provide comic relief, and he is true to form in this play. One example of a comic element is in act 2, scene 2, when Stephano and Trinculo first meet Caliban. Stephano and Trinculo, a butler and a jester, don't know what to make of Caliban, and after Stephano gives Caliban alcohol, Caliban comically wants to worship this foolish and venal servant as a God.

William Shakespeare's The Tempest is considered a comedy, so there are many comical elements within the play.
One of the big ones is the result of the culture shock experienced by Miranda, who has been raised virtually alone with her father on a magical island, when she first encounters sailors from the outside world.
The sailors are clueless about the island where they find themselves shipwrecked and are repeatedly tricked by the mischievous spirit/sprite Ariel, which can lend itself to a fair bit of humor. Specifically, the sailor Alonso, a drunkard and a butler (making him one of the few lower-class characters in the play), fulfills the role that would perhaps be known as clown or fool in one of Shakespeare's other comedies, and his drunken antics give rise to much hilarity.

Calculus of a Single Variable, Chapter 5, 5.7, Section 5.7, Problem 5

Indefinite integral are written in the form of int f(x) dx = F(x) +C
where: f(x) as the integrand
F(x) as the anti-derivative function
C as the arbitrary constant known as constant of integration

For the given problem, the integrand f(x) =1/sqrt(1 -(x+1)^2) we apply
u-substitution by letting u =(x+1) and du = 1 dx or du= dx .
int (dx)/sqrt(1 -(x+1)^2) = int (du)/sqrt(1 -u^2)

int (du)/sqrt(1 -u^2) resembles the basic integration formula for inverse sine function: int (dx)/sqrt(1-x^2)=arcsin(x) +C .
By applying the formula, we get:
int (du)/sqrt(1 -u^2) =arcsin(u) +C
Then to express it in terms of x, we substitute u=(x+1) :
arcsin(u) +C =arcsin(x+1) +C

What are three important quotes from "By the Waters of Babylon" by Stephen Vincent Benét?

I like the second sentence of the story for a good quote.

It is forbidden to go to any of the Dead Places except to search for metal and then he who touches the metal must be a priest or the son of a priest.  

There is so much mystery to the quote because it is placed so early in the story. What are the Dead Places? Why is it forbidden? What's up with the metal phobia, and why can priests touch it? What's great about the quote is that the story slowly answers all the questions it poses and relates them to John. He is the son of a priest and trains to become a priest. The metal must have been loaded with radiation from the "Great Burning," and the Dead Places are former cities that have been destroyed in a disaster or war.  
I also like this next quote.

It is better to lose one's life than one's spirit, if one is a priest and the son of a priest.

John is saying he would rather die trying to follow his dreams and passions than live knowing he didn't try. That thought gives him the courage to cross the Hudson into the former New York City.
The story closes with this next quote. 

At least, we make a beginning. And, when I am chief priest we shall go beyond the great river. . . We must build again.

"By the Waters of Babylon" is a depressing story. This final quote ends the story in a positive and uplifting way, though. Readers get the feeling that John is the right leader to begin the rebirth of learning in his people.

What do you think is the most important theme of Death of a Salesman and why? Discuss the meaning/significance/function of the scene of your choice in relation to the theme of the play.

I would say that Death of a Salesman's most important theme is to be true to yourself and work to develop what you are good at and drawn to, rather than trying to get rich quickly. Willy Loman buys into a version of the American Dream in which he believes he can sit in a hotel room in his slippers, work the phones as a salesman, and earn money that will come rolling in effortlessly. This is an illusion. Tragically for him, he fails as a salesman, ending life with very little money beyond his life insurance policy, passes on his failure to his sons, and misses out on what he might have really enjoyed doing. This is the most important theme because your life can be wasted and the people you care about most hurt if you put earning money ahead of finding and working at a meaningful vocation. Willy has become divorced from reality in his pursuit of an illusion he can't give up.
To illustrate this theme, I would pick the scene in Act II where Willy is having a conversation with his boss, Howard, about getting a raise and an easier work schedule. As Willy persists in thinking he is valuable as a salesman, Howard is trying to fire him. Willy, however, falls back into fantasy, telling Howard the following story:

Oh, yeah, my father lived many years in Alaska. He was an adventurous man. We’ve got quite a little streak of self reliance in our family. I thought I’d go out with my older brother and try to locate him, and maybe settle in the North with the old man. And I was almost decided to go, when I met a salesman in the Parker House . . . . And old Dave, he’d go up to his room, y’understand, put on his green velvet slippers—I’ll never forget—and pick up his phone and call the buyers, and without ever leaving his room, at the age of eighty-four, he made his living. And when I saw that, I realized that selling was the greatest career a man could want.

This passage shows that Willy could have done something else, make a life in Alaska, and perhaps pursue what we suspect he really loves: gardening and working with his hands. Instead, he falls for the illusion represented by Dave Silverman. Willy's problem is that he has never been like Dave Silverman (if Dave Silverman's story is real) but can't accept that, so strong is the power of his dream. 

To which school is David sent?

In David Copperfield by Charles Dickens, David is sent to Salem House as a punishment. Growing up, David lives with his mother and Pegotty, the family's nurse. When David's mother remarries, however, she marries a cruel man named Mr. Mudstone.
Mr. Mudstone despises David and physically harms him often. One day, Mr. Mudstone beats David and David bites his hand. This upsets Mr. Mudstone so much that he sends David off to Salem House.
Salem House is a horrific experience for David because the headmaster of the school, Mr. Creakle, is also a supporter of physical punishment. When David arrives, Mr. Creakle tells David that he heard he was "famous for biting" and he is "famous for biting, too." He then talks about his cane as if it has teeth and asks David if the cane has one sharp tooth or a double tooth. Throughout the series of questions, Mr. Creakle hits David with the cane. Sadly, Mr. Creakle gives the other boys at Salem House similar punishments.

David is sent by his wicked stepfather, Mr. Murdstone, to Salem House school. It's a pretty grim place, to put it mildly. The headmaster, Mr. Creakle, is a brutal, sadistic bully who enjoys dishing out physical punishment to the boys at the drop of a hat. David manages to make some friends there—Tommy Traddles and James Steerforth (although, in the latter case he comes to regret it)—but on the whole it's not a very happy experience for him.
After David goes AWOL from Mr. Murdstone's dark, Satanic bottling factory, his kind Aunt Betsey Trotwood sends him to a school in Canterbury run by Dr. Strong. This is much more to David's liking, not least because Dr. Strong is the very opposite of the revolting Mr. Creakle. He's kind, humane, considerate, and learned—just the kind of man to create an ideal learning environment for the young David.