Why did some Indian Tribes follow the path of accommodation to the white expansion, while others rose in armed resistance?

It was sort of a lose-lose proposition for them, wasn't it?  The answer to this, I believe, lies in a variety of factors I'll try to address in my limited space below:

1)  Cultural differences between tribes - Some were more warlike to begin with or felt more threatened, while others had always dealt with conflict in a more peaceful manner

2)  Time Frame of Contact - Te earliest tribes had little reason to fear the Europeans, or at least, they didn't know to fear them.  The early explorers were small in number and the early settlements barely survived the winters on the east coast.  Later contact, say with the Sioux or Cheyenne in the American West, they had already heard much about whites, smallpox, the US Army and why you shouldn't sign treaties.

3)  Pragmatism - That is to say, some of the wiser chiefs were simply more practical, saw that the whites had overwhelming numbers and strength, and that to other tribes, resistance had been futile.  Why not try and get as much for your people in the future as you can?Given the fact that the US government did not honor the treaties they signed, this may seem foolish, but armed resistance, in the long run, was every bit as unsuccessful if not more so.

Calculate limit (x^2+2x+1)/(2x^2-2x-1), x->+infinity

In order to calculate the limit of a rational function, when x tends to +inf., we'll divide both, numerator and denominator, by the highest power of x, which in this case is x^2.

We'll have:

lim[(x^2+2x+1)/(2x^2-2x-1)]= lim(x^2+2x+1)/lim(2x^2-2x-1)

lim x^2(1 + 2/x + 1/x^2)/lim x^2(2 - 2/x - 1/x^2)

After simplifying the similar terms, we'll get:

(lim 1 + lim 2/x + lim 1/x^2)/(lim 2 - lim 2/x - lim 1/x^2)

lim[(x^2+2x+1)/(2x^2-2x-1)]=(1+0+0)/(2-0-0)=1/2

10 ways in which you can show citizenship.Actions that can be taken.

The previous posts were extremely strong.  I would merely like to add that a vital element of citizenship is being able to strike a balance between preserving realms of positive liberty and negative liberty.  The former has been demonstrated in many of the posts.  The idea of joining a club or an organization, or acting in a manner where one's freedom is exhibited is a strong component of citizenship.  Yet, there is another defining element to citizenship.  This is where individuals acknowledge another's right to be left alone.  To act in a manner free of intimidation, harassment, or social encroachment and to stand for allowing others' sense of negative liberty, to be left alone, is something that is vital to a definition of modern citizenship.  To act in a manner that represents taking a stand against those who seek to overwhelm others' voices is another aspect of citizenship, preservation of a realm or right to be left alone.

In Hamlet, how would one characterize the relationship between Claudius and Gertrude in Act 4 Scene 1?Quote lines.

In Shakespeare's Hamlet, the
relationship between Claudius and Gertrude is as strong as ever in Act 4.1--at least on
the surface.

She immediately tells Claudius exactly what he
asks for:  what do her "sighs" and "heaves" mean and where and how is Hamlet (Act
4.1.1-5)? 

She tells him that Hamlet is
as

Mad as the
sea and wind when both contend

Which is the mightier.  (Act
4.1.6-7)

And she informs
Claudius of the details concerning Hamlet's killing of Polonius, and that Hamlet is
removing the corpse from her chamber.

But she doesn't stop
there.  She also tells Claudius that Hamlet "...weeps for what is done" (Act 4.1.27)--is
sorry for killing Polonius. 

Like much in the play,
however, Gertrude's actions are ambiguous, and thus, while the relationship between her
and Claudius appears to be as strong as ever, there is a possibility that it is
not.

Gertrude, in fact, tells Claudius exactly what Hamlet
asks her to tell him just a few minutes before Act
4.1:

[Don't
let Claudius] Make you to ravel all this matter out,

That I
essentially am not in madness,

But mad in craft.  (Act
3.4.190-193)

Hamlet tells her
to not let Claudius sweet talk her into telling the truth about Hamlet's madness--that
he is only acting.  And she doesn't.  She tells Claudius that Hamlet is as mad as the
wind and the sea when they contend to see which is the most powerful.  Then, as
mentioned, she also defends her son and tries to alleviate the seriousness of what he's
done by telling Claudius that Hamlet is sorry for killing
Polonius. 

Her words are ambiguous, because we don't know
her motivation.  She may tell Claudius that Hamlet is mad because Hamlet asks her to, or
she may tell Claudius that Hamlet is mad because she really thinks he
is. 

Gertrude promises Hamlet that she will do as he
asks:

Be thou
assured, if words be made of breath

And breath of life, I
have no life to breathe

What thou hast said to me.  (Act
3.4.200-202)

She will not
speak the truth about Hamlet's madness.  And, again, she
doesn't. 

Yet, after seeing Hamlet kill Polonius, then
speak to the air as if there is someone present (he sees the Ghost, she doesn't), the
possibility certainly exists that she is merely saying what Hamlet wants her to say, and
that she still believes Hamlet is, indeed, mad.  And one could hardly blame
her. 

Thus, the relationship between Gertrude and Claudius
might be as strong as ever in Act 4.1, or a rift may have developed:  Gertrude may have
switched her allegiance from Claudius to her son, Hamlet. 

Explain the summaries of chapters 1-5 in The Prince and the Pauper.

Chapter I introduces the reader to the two boys born on
the same day in different environments.  one boy is a pauper born to a por family.  The
other child is born to the king and is a young prince.  Tom Canty was the poor boy and
Edward was the rich child.  Tom is mistreated by his father but is still a pleasant
lad.  He has a special friend in Father Andrew.

Chapter 2
finds Tom outside the gates of the castle where he sees a young prince playing in fine
silken robes.  Tom is near the gates looking through when a soldier jerks him away. The
prince sees how the boy is treated and calls for the soldiers to bring him to him.  He
has the boy fed in his quarters and they get to know each other for a brief period.  The
prince is amazed by Tom's telling him about his life for he has had very limited
experiences.  The prince longs to see what it would be like to be free of duties and
stuffy gatherings.  They switch clothing and find that they look just a like.  Later the
soldier throws Edward out of the castle and mistakes him for the
pauper.

Chapter 3 leaves the young prince trying to cnvince
others that he is really the Prince but it does him no good.  He tries to talk down to
people and is soon beat up by some boys.  Tom's drunk father finds him and drags him
home.  He thinks the boy has gone crazy.

Chapter 4 has Tom
back at the palace enjoying his new found wealth and food. However, after the prince
does not return he becomes frightened.  He knells to people he should not and they think
that he has gone mad as well.  Tom tries to tell the truth but it only makes the king
think that the boy is ill as well.

Chapter 5 has Tom
feeling like a prisoner in the castle.  He is dressed and resented like a pet.  He does
not know how to act like a prince and even drinks the water brought to him at the table
for him to wash his hands.  The king is very ill and getting sicker.  He looks for a
seal that the prince had hidden before he left. 

What's a good thesis statement for racism in the book, I, Rigoberta Menchu: An Indian Woman In Guatemala?

Hi!  I haven't read this book, but I can help you come up with a good thesis statement.  Whenever you are looking at a book/topic for a paper, you need to make a list or several lists to help you organize your ideas.  First, what evidence is there of racism in this book?  What events happen or how are people treated?  Are the events or treatment justified in any way by characters in the book?  If so, how?  How do you feel about the examples of racism and/or the justifications of it in the novel?  Now that you have all of these answers, make sure that you make a statement about something that matters to you.  Don't try to write a paper about something just to meet the deadline...it almost always ends up being uninteresting and flat. Be sure to choose a topic that matters to you (if it's teacher assigned, play with it until you can see an angle that interests you).  Also, make sure that what you've written is a thesis--not a topic.  For example:  "Cats in apartments" is a topic.  "Cats make better apartment pets than dogs" is a thesis.  Now you can come up with 3 or more reasons WHY you believe cats make better apartment pets than dogs, and support each reason with anecdotes, quotes, research, or other means.

Good Luck!

In Act IV, Scene 3, what reasons does Claudius give for not taking legal action against Hamlet? What are other reasons?

In Hamlet Act IV, scene iii, the main
reason that Claudius cannot take political action against Hamlet is that the people of
Denmark love him.  Hamlet is the first son of Denmark, a popular prince whom many feel
deserved the crown after his father died. 

Claudius knows
that imprisoning him would be political suicide on his
part:

readability="0">

Yet must not we put the
strong law on him:
He's loved
of the distracted multitude,
Who like not in
their judgment, but their eyes;
And where tis so, the
offender's scourge is weigh'd,
But never the offence. To
bear all smooth and even,
This sudden sending him away must
seem
Deliberate pause: diseases desperate
grown
By desperate appliance are
relieved,
Or not at
all.

Literally
translated, this means:

readability="15">

Yet we must not put the strong law
on him.
He's very popular with this country’s
masses,
Who like not in their minds, but with their
eyes,
And where it is so, the offender's punishment is
important,
but never the offense. To deal with everything
smoothly and evenly, this
sudden sending him away
must seem like a planned event. Diseases
grown
desperate are best healed by desperate measures,
Or not at
all.

Claudius says that the
people value appearance over reality.  What a hypocrite!  He's saying the people only
like Hamlet because he's young, blond, and hot. 

Who knew
Hamlet was like an older version of Prince William?