# Search results

1. ### WHat's wrong in my argument?

I was asked to prove, every punctured open set in R^2 is path connected. My argument : take points x and y. let z be the point we've taken off from U (open). if x, y,z do not pass through a staright line, we have a segment between a and y. Now if the 3, i.e. x,y,z lie on a straight...
2. ### Assume that f is non-negative on (0,1)

Hello...I need help and I know this is a very simple problem...I don't know why I'm getting stuck( Maybe because it's past midnight here:frown: ) Assume that f is non-negative on (0,1) and the third derivative of f exists on (0,1).If f(x)=0 for at least 2 values of x in (0,1), show that there...
3. ### Integral problems

sin^k(x)=(sinx)^k =sinx *sinx*.......k times and to express the second one let f(x)=sinx then f^k(x)= (sin(sin(....sin(x)))....))
4. ### Integral problems

thanks for the help... never mind the second one...i figured it out.
5. ### Integral problems

the former...
6. ### Integral problems

i think i don't have adequate theory to solve these problems.... :frown: 1.given that f(x) =cos(x) sin^k(x) / (1+x). calculate integral of this function wrt x between limits 0 and pi/2 . then find the it's limit as k tends to infinity... 2.let f(x)={e^(-ax)-e^(-bx)}/x, 0< a< b .let I be...
7. ### Green's Theorem

thanks...trust me,that DID help...
8. ### Green's Theorem

thanks...but just to make it clearer,can you give me another set of of values of P and Q?
9. ### Green's Theorem

find the double integral of the function e^(x^2) over the region where y/2 <= x<= 1 and 0<=y <=2 USING GREEN's THEOREM. I can't imagine how we'd use green's theorem here...if F=(P,Q) is the function, are we supposed to find P and Q using green's theorem and then parametrize the boundry of...
10. ### Set closure and interior points

yes....you've got it right...