Notes

Given to solve, `lim_(x->oo) sinx/(x-pi)` This can be solved by applying the squeeze theorem and is as follows as we know the limits or boundaries of `sin(x)` is `-1<=sin(x)<=1` Dividing the above expression with x-pi we get `-1/(x-pi)<=sin(x)/(x-pi)<=1/(x-pi)` now, let us apply the limits that` x-> oo` we get `lim_(x->oo)(-1/(x-pi))<=lim_(x->oo) sin(x)/(x-pi)<=lim_(x->oo) 1/(x-pi)` but `lim_(x->oo)(-1/(x-pi)) = -1/(oo -pi) = 0` `lim_(x->oo)(1/(x-pi))= 1/(oo -pi) = 0` so, `0<=lim_(x->oo) sin(x)/(x-pi)<=0` so , `lim_(x->oo) sin(x)/(x-pi) = 0`

In the book To Kill a Mockingbird, Scout definitely struggles with the social expectations that are placed on her. Though she is young, the people around her are constantly attempting to remind her that she is supposed to be acting like a "lady." In the book, she is considered a tomboy; she gets in fights, she dresses differently than other girls her age, and she asks tough questions that make people embarrassed and more considerate of their own actions. All of these are things that a young lady in the old South would not have been encouraged to do. At the time, it was the belief of most people, especially older folks like Aunt Alexandra's friends, that children should be "seen and not heard," "speak when spoken to," and act "ladylike," which includes wearing dresses, staying out of the dirt, and keeping one's hair combed and neat. None of these cultural and social expectations are things that Scout wants to do, and, in fact, she feels th...

Carl Jung was the psychoanalyst who first discussed the concept of the “shadow self.” The shadow self represents the dark sides of our personalities, where we keep all the thoughts, impulses, and desires that society or our own moral code find unacceptable or even evil. Our shadow self can also house realities we deny because they are too painful or frightening to face. In “The Masque of the Red Death,” Edgar Allan Poe introduces us to Prince Prospero. In his country, a plague has broken out and is decimating the population. It is a fast-moving plague, characterized by sudden sharp pains, followed by “profuse bleeding at the pores.” Once struck, the victim is dead within thirty minutes. Prospero decides to try to cheat Death by gathering a thousand of his friends and closing them in his castle with him. He ignores the needs of his country and focuses on his own self-preservation. For six months, the prince and his chosen fellow survivors live well in the castle. Prospero has taken care...

In the sixth paragraph of Ernest Hemingway's "A Very Short Story," Luz begins a relationship with the major of the battalion in Pordonone, after the soldier leaves Genoa for America. In the letter she writes to the soldier about her new relationship, she describes her previous relationship with the soldier as "a boy and girl affair" and "a boy and girl love." She draws this conclusion by comparing the soldier to the major, who she says intends to marry her in the spring, although he never does. Luz assumes her relationship with the major is more mature and serious than her previous affair with the soldier, which she considers childish in retrospect, but this assumption is never proved true when her new relationship doesn't end in marriage.

The Civil War was a very costly war and had significant consequences. The greatest sacrifice was in terms of the lives that were lost. About 620,000 Americans died in the Civil War. The total amount of money spent was about $2.3 billion. Much of the South was destroyed, and it would take years to rebuild the South. There were important consequences as a result of the Civil War. Slavery ended as a result of the Civil War. It also became clear that the federal government came first while the state governments came second. The Civil War showed Americans that there had to be a better way to resolve our disputes than to fight each other. The enormous cost of the Civil War made this point very clear. As a result of the Civil War, the South had to be rebuilt. This gave us an opportunity to create a society that was better than what we had before the Civil War began. While conditions improved for a while in the South for African-Americans, eventually some of the lessons from the war were lost ...

Although Paul's mom says almost nothing, directly, about the house she grew up in, her comments in the chapter titled "Thursday, August 31" strongly imply that she grew up in a very small and/or very run-down house in a poor neighborhood: Mom suddenly got very serious. "Paul, I'm talking as somebody who never, ever lived in a nice house growing up. Or even lived anywhere near a nice house. This is not a joke to me. Your house is your family's biggest investment. And you have to protect that investment." The home that the Fisher family has moved into in Tangerine is clearly very nice, representing the upper middle-class lifestyle that the family enjoys. There's a guardhouse at the front of the neighborhood, everything is newly built, and each of the boys gets his own room in the house. By contrast, Paul's mom was definitely not raised in such luxury when she was a child. This comes up in the novel because Paul finds it strange that his mom is so w...

The fact that Pony wants the broken bottle shows that he is scared.   Johnny and Pony ran into a few Soc girls at the movies, Cherry and Marcia.  The girls were nice enough, but their boyfriends were trouble.  The Soc boys did not want their girls hanging out with a couple of greasers.   On the way back from the movies, Bob’s car drove up and the girls were worried about what would happen if their new friends and their boyfriends mixed it up.  Knowing there could be trouble, Two-Bit handed Pony a broken bottle to use as a weapon.  Cherry told Bob the girls would get in the car, and the crisis was temporarily averted.  Two-Bit questions whether Pony would have been able to fight if he had to.  "I don't know why I handed you that busted bottle," Two-Bit said, getting to his feet. "You'd never use it." "Maybe I would have," I said. (Ch. 3)   This is a reference to the fact that Pony is not really a fighter.  Johnny was terrified by the car, because he...