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  1. M

    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. M

    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. M

    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. M

    Integral problems

    thanks for the help... never mind the second one...i figured it out.
  5. M

    Integral problems

    the former...
  6. M

    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. M

    Green's Theorem

    thanks...trust me,that DID help...
  8. M

    Green's Theorem

    thanks...but just to make it clearer,can you give me another set of of values of P and Q?
  9. M

    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. M

    Set closure and interior points

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

    Compactness contradiction physics

    thanks a lot...i figured that out finally!
  12. M

    Compactness contradiction physics

    thanks.... i did do the sequences thing but i feel that it's not an elegant way of doing it. why? that's because you're talking about distance in A (cross) A that's what d(an,bn) means... so i think it's definitely not the best way of doing it.... "every continuous real valued function on...
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    Compactness contradiction physics

    Let A be a compact subset of a metric space (X,d). Show that there exist a,b in A such that d(A) = d(a,b) where d(A) denotes the diameter of A. I guess...we're supposed to use the fact that a compactness of A implies that it is closed and bounded or alternately...we could assume that...
  14. M

    2 functions f,g:X -> X that are discontinuous

    2 functions f,g:X --> X that are discontinuous looking for 2 functions f,g:X --> X that are discontinuous but their composition gof continuous...
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