Why does Amir recalls the memory of the lamb being sacraficed when he witnesses Hassan's tragedy in the alleyway?Amir recollects the memory again...

I have a little different take on why Amir's mind flashes
back to the sacrificial lamb during the attack on Hassan in Chapter 7.  At this point in
the novel, Amir is at a crossroads--he so desperately wants Baba's approval, that he
must decide what he is willing to sacrifice to get it.

As
he comes upon the scene in the alley, Amir knows that Hassan is so loyal to him that he
will sacrifice himself to keep the kite for Amir.  However, Amir is actually the one in
charge of the sacrifice; he could choose to step in or call for help, but he does
neither.  Instead, he makes the conscious decision to sacrifice Hassan's innocence and
peace of mind so that he can obtain Baba's approval.

The
image of the literal lamb being led to the sacrificial slaughter is something that
always horrified Amir, and so his memory of it in Chapter 7 demonstrates that Amir knows
just how harmful his choice to sacrifice Hassan is. Hosseini includes this flasback on
purpose; so look for other examples in The Kite Runner of Amir's
dreams or memories illuminating his guilty conscience.

What is the limit: lim x-->0 [(sqrt (1+x) – 1 –(x/2)) / x^2]

First, we'll substitute x by the given value 0, in the
expression of the limit:

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

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

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

We've obtained an indeterminacy case
0/0.

We'll apply L'Hospital
rule:

lim f'(x)/g'(x) = lim
f(x)/g(x)

f'(x) = [sqrt (1+x) – 1
–(x/2)]'

f'(x) = (1+x)'/2sqrt(1+x) - 0 -
1/2

f'(x) = 1/2sqrt(1+x)-
1/2

g'(x) = 2x

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

We'll
substitute x by 0:

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

Since we've obtained again an
indeterminacy, we'll differentiate the result:

f"(x) =
[1/2sqrt(1+x)- 1/2]'

f"(x) = [-2/2sqrt(1+x)]/4(1+x) -
0

f"(x) =
[-1/sqrt(1+x)]/4(1+x)

g"(x) =
2

lim [1/2sqrt(1+x)- 1/2]/2x =
lim  -1/8(1+x)sqrt(1+x)

We'll substitute x by
0:

 lim  -1/8(1+x)sqrt(1+x) =
-(1/8)*(1/1)

 lim [(sqrt (1+x) – 1 –(x/2)) /
x^2] = -1/8

if a sum of money grows to 144/121 times when invested for 2 years in a scheme where the interest is compounded annually ,then how long will the...

The principle P becomes 144/121 times in 2 years in a
compound interest annual.

Therefore  P(144/121) =
P(1+r)^2

144/121 = (1+r)^2.

We
take square root.

12/11 =
1+r

12/11 -1 = r

r =
(12-11/)11 = 1/11.

Therefore (100/11)% is the rate of
annual interest.

So for n years the simple interest =
Pnr/100 = Pn (100/11)/100 = Pn/11.

So along wirh principle
and the interest ,the amount  P+Pn/11

If it takes n years
to triple the ampount , 3P = P+Pn/11

3 =
1+n/11

n/11 = 3-1=2

n = 2*11 =
22.

Therefore it takes 22 years for the Principle along
with a simple interest of (100/11)% PA to become 3 times
itself(principle)

What do the gooseberries in Chekhov's short story "Gooseberries" symbolize?

In Anton Chekhov's short story "Gooseberries," part of a
unique trilogy including "The Man in the Shell" and "About Love," the gooseberries are
part of complex theme that is both metaphysical and practical and is summed up in Ivan
Ivanovich's plea, "Don't be calm and contented! Don't let yourself be put to
sleep!"

Nicolay has managed to improve his position in life
after his wife's death and buys himself the estate he has always dreamed of owning
complete with bushes of luscious gooseberries. Years later when Ivan Ivanovich visited
Nicolay, he found that Nicolay was corpulent and happy in his vast enjoyment of his
country life and gooseberries.

Chekhov introduces
contemplation of the woes and miseries of life as represented in drunkenness, pain,
degenerate living, poverty and its attendant hunger and these contemplations stand in
stark contrast to the luxurious happiness of gooseberries. Chekhov thus equates
gooseberries with luxury, contentedness, self-serving happiness, and obsession with
personal dreams.

Gooseberries prevent a person from
recognizing and contributing to the solution of pain and evil in the world. Thus
gooseberries symbolize a two-part theme. Firstly, they symbolize the metaphysical theme
of truth and meaning in life: Is individual contentedness and happiness the truth and
meaning in life? Secondly, they symbolize the practical theme of human responsibility to
alleviate suffering in life.

How does the doppler effect work?

The Doppler Effect is an observed change in the frequency
of any wave when the source of the wave is moving. When the source of a wave moves
toward the observer, each disturbance reaches the observer in a time less than the
previous disturbance one. And when the source moves away from the observer the time
taken for each disturbance to reach the observer is more than the earlier one. This
causes an increase in the frequency of the wave when the object and source are moving
closer for a href="http://www.exploratorium.edu/hubble/tools/doppler.html">blueshift and
a decrease in the frequency when the object and source are moving away from each other
for a href="http://www.exploratorium.edu/hubble/tools/doppler.html">redshift. The
Doppler Effect can be observed in all types of waves like sound, light, etc. One popular
application of the Doppler Effect is in measuring the speed of
objects.

What motivates the narrator to overcome his distinctive antipathy to the blind man in "Cathedral"?

In the story "Cathedral" the man is unhappy about having
to entertain a blind person.  He seems uncomfortable at having to figure out how to
relate to the man and does not really view the blind man as
normal. 

The two men relax in the evening and eventually a
beautiful cathedral comes into view on the television.  When the blind man asks the man
to describe it, he finds that he does not have the ability to describe such a thing of
beauty in a way that someone blind can relate to it. The blind man asks him to draw it,
but the man feels that he is inferior in art.  The blind man takes the man's hand as he
draws the cathedral. 

The act of the man drawing the
cathedral and taking the blind man on a journey of movement connects them in a very
different manner.  The man is amazed that by drawing he is sharing the experience with
the blind man which opens himself up to seeing things in a new way as
well.

If both where origniated by English origin. Why did the New England and Chesapeake region evolve into two distinct societies?

I think geography played an important role in the two
distinct societies that developed in New England and in the Chesapeake region.  The
Chesapeake region had the geographic characteristics that include rich soil, mild
winters, a long growing season, and abundant rainfall.  This led the Chesapeake region
to become primarily agricultural, growing the most crops and the greatest variety of
crops.  This in turned led to the creation of large plantations and the reliance on
slave labor, which defined southern society. The New England colonies had thin rocky
soil, harsh winters, a short growing season, cold coastal waters, and good harbors. 
This led New England to rely more on manufacturing and commerce as compared to the
Chesapeake area, including shipbuilding, ironworks, lumbering and fishing.  Slavery
became less important in that area.  This in turned led to a different type of society
than the Chesapeake area.