What are some quotes about family in The Catcher in the Rye?

The Catcher in the Rye is full of quotes about family. Here are three to start, with a little information about each of them.
The very first sentences of the novel are about family:

If you really want to hear about it, the first thing you'll probably want to know is where I was born, an what my lousy childhood was like, and how my parents were occupied and all before they had me, and all that David Copperfield kind of crap, but I don't feel like going into it, if you want to know the truth. In the first place, that stuff bores me, and in the second place, my parents would have about two hemorrhages apiece if I told anything pretty personal about them. They're quite touchy about anything like that, especially my father.

This passage reveals Holden's attitude towards his own early life, or at least, it reveals how Holden feels about talking about his childhood. Here as well the reader can find some interesting information about how Holden perceives his parents and their protectiveness of their privacy.
Later in the novel, in part 5, Holden mentions his brother:

He's dead now. He got leukemia and died when we were up in Maine, on July 18, 1946. You'd have liked him. He was two years younger than I was, but he was about fifty times as intelligent. He was terrifically intelligent. His teachers were always writing letters to my mother, telling her what a pleasure it was having a boy like Allie in their class. And they weren't just shooting the crap. They really meant it. But it wasn't just that he was the most intelligent member in the family. He was also the nicest, in lots of ways.

This passage is also revealing as Holden is somehow simultaneously open and honest about a very sensitive family tragedy, while he is cagey about his family at the same time. He doesn't describe the not-nice behaviors in any detail, but the reader knows that they exist.
This passage about family can be found in part 15:

My father's quite wealthy, though. I don't know how much he makes––he's never discussed that stuff with me––but I imagine quite a lot. He's a corporation lawyer. Those boys really haul it in. Another reason I know he's quite well off, he's always investing money in shows on Broadway. They always flop, though, and it drives my mother crazy when he does it. She hasn't felt too healthy since my brother Allie died. She's very nervous. That's another reason why I hated like hell for her to know I got the ax again.

Holden is clear here about his guilt and his sense of responsibility for his mother's happiness, but he is less clear about how he feels about his father and his father's career. This lack of transparency makes for some interesting opportunities for literary analysis as the reader can go in a lot of different directions with the evidence here.

Why is the story called "Dusk"?

What a great question. I believe the short story "Dusk," by Saki has its title for a two-fold reason. The setting is around 6:30 on a March evening in Hyde Park: dusk. But more importantly, I believe Saki is commenting on our inability to actually see others.
The protagonist, Norman Gortsby, is a cynical man who reckons himself perceptive, aware of the plight and motives of other people. He enjoys sitting in Hyde Park at dusk watching the people go and come. He presumes those who leave have places to go while those who come are defeated in some way.
He immediately thinks an old man sitting near him one of these defeated people, yet the old man gets up and leaves. When a young man sits next to him, indeed sounding defeated, Norman asks him what is wrong, and the young man tells him that he has forgotten which hotel he was staying in when he left to buy soap and that now he is stuck in a strange city with nowhere to sleep. He hopes some kind stranger will help him out so that he can sleep in a safer place.
Though the story sounds convincing, Norman, cynical as usual, is convinced that the young man is a clever panhandler trying to trick strangers into giving him money that he will never repay. When the young man cannot produce his bar of soap, Norman feels justified in his judgment and the young man leaves. But when Norman notices a small cake of soap on the ground near the bench, he feels terrible for having not seen the truth about this young man's honesty, tracks him down, and loans him some money. Feeling good about this faith-restoring encounter, Norman returns to his bench only to find the old man whom he had earlier presumed was defeated searching for his lost cake of soap. Ironically, Norman's enlightenment has only served to darken his outlook.
Dusk can represent a number of things symbolically, but in this case I think it represents not only Norman's inability to fully see the truth in either of the men, but also his dim, cynical outlook on life, which is only reinforced by the young panhandler's swindle that left Norman defeated. Saki is telling us to be careful whom we trust, but he's also telling us that trusting can give us a kind of joy that cynicism cannot. We are faced with a choice. Either we darken our hearts a little as we learn through experience not to trust other people, or we choose not to see so that we can believe in others. Either way, the outlook is dim, and we are always in the dusk.

In the novel Three Men in a Boat, Jerome was medically ill. Do you agree?

No, the character-narrator of the book, J., is not medically ill. He may be a hypochondriac, though, and he may just believe that he is sick. Or at least, J. has a quick inclination to become sick when this possibility is suggested to him.
In the first chapter, J. shares the story of his trip to the British Museum as a way of illustrating his approach to life. Here he consults the medical reference book and quickly believes that he is afflicted with almost all of the diseases described in it. Is this even possible in real life? Of course not. As usual, J. overreacts, or he misinterprets information and experiences that come his way. This early story quickly unveils to us some of the personality quirks of this character. He also tells it in a humorous way, setting the stage for many more odd encounters and humorous situations to come. Three Men in a Boat is full of such scenes. It makes for enjoyable reading.

Calculus: Early Transcendentals, Chapter 7, 7.4, Section 7.4, Problem 8

int ((3t-2)/(t+1)) dt
sol:
let t+1 = u
=> t= u-1
=> dt =du
int ((3t-2)/(t+1)) dt
= int ((3(u-1)-2)/(u)) du
= int ((3u-3-2)/(u)) du
= int (3u-5/u) du
= int (3- (5/u)) du
= int 3 du - int (5/u) du
= 3u - 5*ln(u)
= 3*(t+1)- 5*ln(t+1) +C
:)

Why does Darry now hate Paul Holden?

Paul Holden is Darry's former friend and Soc member, the first to challenge Darry at the start of the rumble. Pony mentions that Paul had played halfback on Darry's football team and used to be close with his oldest brother. Unlike Darry, whose parents died in a tragic accident and who was forced to abandon his dreams of playing college football in order to raise Pony and Soda, Paul was fortunate and had the opportunity to enroll in college.
As the two boys stare each other down, Pony notices that Paul views Darry with hate, contempt, and pity. Darry hates and envies Paul because he was given certain advantages and opportunities in life. While Paul continued to play football and earn a college education, Darry was forced to work two jobs and struggles to make ends meet. Darry also hates the fact that he is representing the Greasers, which Pony understands is a source of shame. Overall, Darry is jealous of Paul's fortunate life and resents the fact that Paul was given so many opportunities while he was forced to work to support himself and his family and abandon his dreams.

At the rumble between the Socs and the greasers, Darry steps forward to start the fighting, saying "I'll take on anyone." When Paul Holden responds to Darry's challenge, Ponyboy hears Soda react with surprise and perhaps dismay, and Ponyboy recognizes Paul as Darry's old friend from his football days. According to Ponyboy, they hate each other now, despite sharing history and good times in the past: "[t]hey hate each other because one has to work for a living and the other comes from the West Side."
Ponyboy blames their hatred on the differences in their positions in society, which have nothing to do with them as people. In the time since Darry and Paul were friends, a lot has happened to Darry; he lost his parents and took on the responsibility of his younger brothers, and so much of his potential to do more with his life was lost. Paul, on the other hand, seems to have enjoyed the privilege of his position and attended college, something that may have interested Darry once. Darry's hatred of Paul may come from a feeling of envy and resentment that Paul might not even appreciate everything that he has.

Does Dimitri marry Katerina?

Having seduced Katerina—or Katusha, to use the diminutive by which she's known—Prince Dmitri wishes to atone for his sins. When Katusha is sent to a Siberian penal colony after being convicted of murder, Dmitri becomes ever more determined to change, to affect a deep spiritual transformation within his soul. To this end, he tries his best to help Katusha, following her to Siberia and pulling strings to make sure that she's housed with the political prisoners, well away from the serial criminals who try to take advantage of her.
Moreover, Dmitri wants to marry Katusha, but it's all for the wrong reasons. Dmitri doesn't truly love Katusha; he simply wants to cleanse his soul. Marrying Katusha will be a means to a selfish end, nothing more. For her part, Katusha isn't interested. If she's going to marry, then it will be for love. So she declines Dmitri's proposal, opting instead to stay with Valdemar Símonson, a political prisoner whom she meets in Siberia.

The word “ring-giver” is an example of a kenning. What are some other examples of kennings in Beowulf?

In relation to Anglo-Saxon literature, a "kenning" can be defined as a metaphorical phrase or compound word used to name a person, place, or thing. Kennings abound in Beowulf; the poem's four-beat alliterative lines allow for a huge variety of them to be used. As well as "ring-giver," we have "battle-sweat" meaning blood. And in his brutal epic encounter with Grendel's Mother, Beowulf does indeed shed a fair amount of battle-sweat. Another one is "sail road" meaning the sea. If you think about it, a sail road is exactly what the sea is to Anglo-Saxon warriors like Beowulf. They routinely set sail upon the high seas to trade, fight battles, and explore new lands.
"Sleep of the sword" is a particular favorite of mine. You won't be surprised to discover that it means "death." Notice how two concepts have been yoked together: the sleep of death and the method used to bring it about. Like "battle-sweat" and "sail road," "sleep of the sword" provides us with a glimpse into Anglo-Saxon culture, where death, especially to brave and noble warriors, often came at the end of a sword.

Kennings are compound metaphors common in literature derived from Old Norse linguistic traditions. Functionally they appear may appear frivolous or unnecessarily abstract, but are intended to provide imagery and dexterity to the poet in order to avoid repeating words or to improve the narrative creativity of the work. "Ring-giver" is intended to emphasize the role of a king or leader as a benefactor and source of reward for good service, rings (or torcs, a type of collar or necklace) being a form of jewelry that often conferred status.
Kennings are found throughout "Beowulf" and comprise a significant portion of the text, both in narrative illustration and word count. "Ring-giver" is found on line 1102, and others in this portion of the text include "hate-bites" on 1122, referring to wounds, and "battle-light" on 1142, referring to a sword. 
http://www.heorot.dk/beowulf-rede-text.html