isi 2010 Q23

[eco'17]

http://economicsentrance.weebly.com/uploads/1/1/0/5/1105777/msqe2010.pdf

I started this question with r(X)= P(x)/Q(x) now f(1)=1 implies P(1)=Q(1) we are suppose to find r(2)
I'm stuck here!.......please help

[Abhitesh]

We have to prove that f(x) is constant.
Let us to this by contradiction. Assume that f(x) takes two different values for different x.
Let these values be a and b(>a)
Since f(x) is continuous so it will assume all values between a and b, including the irrational ones.
Which is not possible. Thus f(x) must be constant.
i.e. f(x) =1 for all x in [0,3]

[eco'17]

thanks a lot,
I should have realized that f(x) has to be a constant.
Also, if you don't mind, can you answer Q24 as well?

[Abhitesh]

Find f(ax1, ax2) .Note to change the limit as well.
Substitute w' = w/a.
=> dw = adw'
Limits : w=0 => w'=0 ; w=a*sqrt(x1^2 + x2^2) => w' = sqrt(x1^2 + x2^2)
The integral is same as f(x1, x2). So f(ax1, ax2) = a*f(x1, x2)

[eco'17]

I'm not able to comprehend the answer, please can you explain it again.

[Abhitesh]

Q9.pdf

[eco'17]

okay I think I got it, thanks a lot!