What was the difference between Roman and Athenian governments?

Athens and Rome have had many governments throughout their history. I will assume that this question is referring to Classical Athens in the fifth century BCE and the Roman Republic.
While both governments were republics, meaning there was no king and the (male) citizens had a say in their laws, there are some marked differences between democratic Athens and the Republic of Rome.
First off, Athens was a direct democracy. This meant that citizens voted directly on issues, instead of having members of the government make the decisions. Any adult male citizen had the right to present issues and vote in the assembly. This process is not unlike voter initiatives today. If enough votes for a new law are cast, then it becomes part of the legal code.
The Roman Republic, on the other hand, was a representative democracy. Like Congress in the US, elected leaders make the important decisions, not the rank and file of the citizens. In Rome, a citizen voiced their opinions through the use of elected senators and magistrates.
When it came to political leaders, the Athenians picked theirs by lot. Any adult male citizen was eligible to serve as one of the nine council presidents. The Roman senators were voted on by the citizens. They had to campaign for office and run for election. Rome had separate councils for upper-class citizens (patricians) and lower-class citizens (plebians). Conversely, Athens did not make class distinctions in its government (though it did have strict rules about who was considered a "citizen" eligible to vote).
The reason for the difference in systems probably has to do with size. Athens was a city-state, while Rome was the capital of a vast republic. The population of Athens numbered in the tens of thousands, while Rome had perhaps millions of citizens throughout its many territories during its height. Being a representational democracy allowed Rome to streamline the democratic process.
https://www.ancient.eu/Athenian_Democracy/

https://www.ancient.eu/Roman_Government/

What is a timeline of Bud, Not Buddy by Christopher Paul Curtis?

The story is told from Bud's perspective, so a timeline of events closely follows everything that happens to Bud.  
Bud finds out that he is being placed with a new adoptive family.  He is going to have an older brother, and Bud knows that means trouble. 
Todd Amos and Bud get into a fight.  Mrs. Amos believes everything that Todd tells her and locks Bud in the shed.  
Bud escapes from the shed and gets revenge against Todd by getting him to urinate in bed while sleeping.  
Bud goes to the mission to get a free meal. 
Bud goes to the library to find Miss Hill.  She is not there, because she got married and moved to Chicago. 
Bud and Bugs are reunited and decide to make their way west together by riding the trains.  
The two boys arrive in Hooverville.  Bud meets Deza Malone and gets his first kiss.  
Bugs gets on the train, but Bud misses it.  
Bud decides that he is going to find his father, and Bud believes the best place to start is Grand Rapids.  
Bud begins walking to Grand Rapids at night and is picked up on the side of the road by Lefty Lewis.  
Lewis agrees to take Bud to Grand Rapids.
Bud meets Herman Calloway and claims that Calloway is Bud's father.  Calloway denies it, but Bud is allowed to travel with the band.  
Eventually Bud and Calloway do figure out that they are related.  Calloway is Bud's grandfather, and Bud finally finds the home and family that he has been missing since his mother died. 

Southern literature often focuses on masculine identity, as seen in Tennessee Williams's A Streetcar Named Desire and in Lillian Hellman's Toys in the Attic. Compare and contrast Mitch in A Streetcar Named Desire to Julian in Toys in the Attic. State the similarities, then the differences.

Mitch, from Tennessee Williams's A Streetcar Named Desire, and Julian, from Lillian Hellman's Toys in the Attic, do share some interesting similarities. Neither man seems impressed with money. Mitch lives at home with his ailing mother, and Julian simply shrugs off the fact that he lost the shoe factory he owned in Chicago. Both are committed to their families. Mitch wants nothing more than to take care of his mother, illustrated by his unwillingness to partake in many of the same things that other characters do. Julian, after coming back home, relies on the affection given to him by his sisters.
Essentially, this is where their similarities end. Mitch, seems to take life far more seriously than Julian does. He works hard to take care of those around him, like his mother and Blanche (at least while he and Blanche are dating). He is grounded in his life, illustrated by his working in a factory for many years. He knows what his responsibilities are, and he does not look at them with any disdain. He appreciates life because he has experienced loss (the death of a girlfriend and the impending death of his mother).
Julian, on the other hand, does not take life as seriously or look at it with as much appreciation. He loses money and jobs, shirking any responsibility for the losses. His sisters are the ones who take care of him, although his wife has money as well. It seems that he wants to be taken care of by the women in his life, whereas Mitch wants the opposite.

Julian in Hellman's play Toys in the Attic and Mitch in Williams's A Streetcar Named Desire are similar in that they are both devoted to female members of their families. Julian's two sisters, Anna and Carrie, dote on him and sacrifice for him, and Mitch is oddly connected to his elderly mother. Mitch explains during a poker game, "I gotta sick mother. She don't go to sleep until I come in at night" (Scene 3). He doesn't enjoy going out at night because he worries about his mother, and, similarly, Julian's ties to his sisters bring him home after his marriage to Lily. Both characters seem superficially sensitive to the women in their lives.
However, neither man is truly sympathetic. Julian is careless with the money his sisters give him. To tell them about how he's lost the shoe factory he invested their money in, he says, "Oh, that shoe factory. It's gone" (page 22). While he is off investing in a failed shoe factory, his sisters wear worn dresses, about which he thoughtlessly remarks to Anna, "The same dress?" (page 21). Mitch is similarly not as sensitive as he first appears. While a sense of guilt brings him home to his mother, he is actually insensitive. When Blanche tells him that the inscription that a dying girl wrote on his cigarette case is touching and that sick people have "deep, sincere attachments," Mitch responds, "that's right, they certainly do" (Scene 3). Mitch appears to be sensitive, but he is actually too unimaginative and commonplace to really feel sensitivity.
Mitch and Julian are different in that Julian is far more imaginative than Mitch. After he returns home with money, he wants Gus to buy a farm and tries to encourage his sisters to go abroad. He says, "Ah, can't I be romantic for a month" (page 53). Unlike Julian, Mitch is not imaginative. When he is faced with the reality of Blanche's past and her age, he deserts her. He is not a romantic like Julian and is swayed more by societal ideas about Blanche than by his sense of devotion to her.

int e^(-3x)sin5x dx Find the indefinite integral

We shall use partial integration:
int u dv=uv-int v du  
Therefore, we have
int e^(-3x)sin5xdx=|[u=e^(-3x),dv=sin5xdx],[du=-3e^(-3x)dx,v=-1/5cos5x]|=
-1/5e^(-3x)cos5x-3/5int e^(-3x)cos5xdx=|[u=e^(-3x),dv=cos5xdx],[du=-3e^(-3x)dx,v=1/5sin5x]|= 
-1/5e^(-3x)cos5x-3/25e^(-3x)sin5x-9/25inte^(-3x)sin5xdx                                                                                  
We can see that we have the same integral as the one we've started with. In other words we have the following equation
int e^(-3x)sin5xdx=-1/5e^(-3x)cos5x-3/25e^(-3x)sin5x
-9/25inte^(-3x)sin5xdx
Let us add 9/25int e^(-3x)sin5xdx to the whole equation.
34/25int e^(-3x)sin5xdx=-1/5e^(-3x)cos5x-3/25e^(-3x)sin5x  
Now we only need to multiply the whole equation by 25/34 to obtain the solution to our starting problem.
int e^(-3x)sin5xdx=-5/34e^(-3x)cos5x-3/34e^(-3x)sin5x+c, c in RR                                                                             
https://en.wikipedia.org/wiki/Integration_by_parts

Calculus: Early Transcendentals, Chapter 2, 2.2, Section 2.2, Problem 35

We can also put it in this way
lim_(x->2pi^-) xcsc(x)
=lim_(x->2pi^-) (x) * lim_(x->2pi^-) csc(x)
=(2pi) *(lim_(x->2pi^-) csc(x)) -----------------------(1)

As
lim_(x->2pi^-) csc(x) =lim_(x->2pi^-) 1/(sin(x)) = 1/(-0) = -oo
So, from (1) we get ,
(2pi) *(lim_(x->2pi^-) csc(x))
= (2pi) *(-oo)
= -oo is the infinite limit

In Chapters 13-19, Nomi decides that Tash’s drinking and staying out late are not as serious rebellions as “that library card of hers.” Why is getting a city library card a sign to Nomi that Tash has “gone too far” (120)?

Tash, Nomi's older sister, begins rebelling from the family. Nomi, a Mennonite girl, recounts the way in which Tash and Nomi's mother, Trudie, were excommunicated from the church. Tash, who has a significant impact on Nomi, uses her library card to bring home books "not by Billy Graham," as Nomi says (page 119). Instead, the books that Tash checks out of the library are "pamphlets about communism and Albania being a great place" (page 119). From her reading, Tash learns about the concept of a metaphor and "started applying it to almost every aspect of her life, and ours" (page 120).
Clearly, Tash's reading has made her question the life her family lives and their religious beliefs. Nomi feels that Tash has "gone too far" because Tash is moving beyond their world. Nomi says that Tash's embrace of communism and metaphors represents an even greater rebellion than everyday teenage rebellions such as drinking or staying out with boys because Tash's mindset has become more radical, and Tash has begun to reject the fundamental principles of their family's existence. Nomi even wonders if Tash has become possessed by the Devil, and Nomi begins biting herself out of confusion and pain. 

Why do Elie and his father leave Buna?

They really have no choice in the matter; either they must leave or stay put in the infirmary. And that's no choice at all because both Elie and his father are convinced that the SS will not let them live. Rumors have been swirling around the camp that the Red Army are fast approaching. The Germans decide to evacuate the camp; it's now only a matter of time before the Russians arrive. Having treated Russian prisoners of war so appallingly, the Germans can expect the same treatment if they fall into enemy hands.
Elie and his father figure out that if they leave with the Germans, they still have a much better chance at survival than if they stay behind in the infirmary. They'll be put on a forced march, one that will be brutal and unforgiving, but they feel that this is their best shot at making it through their terrifying ordeal. More than anything else, they want to live, and this they feel is the best course of action.