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Math Help - limit problem

  1. #1
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    limit problem

    Define f: (-1,1) -> R by f(x) = x+1/x^2-1. Does f have a limit at 1? Justify

    I believe that there is no Limit at 1 their is an asymptote at 1 because if I factor I am left with 1/x-1. Am I able to say is this proof good enough to say this or do i need to prove tis a different way

    Assume there is a Limit of f at 1 Choose E = 1/4. There is a @>0 such that if
    0<abs(x-1)<@ then abs(f(x)-L) < 1/4 choose a p= -@/4 and q= @/4 then f(p)= -1
    f(q)= 1 so 2 = abs(f(p)-f(q)) <= abs(f(p)-L) + abs(L-f(q))< 1/4 + 1/4 = 1/2
    Last edited by schinb64; March 6th 2007 at 05:33 PM.
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  2. #2
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    Quote Originally Posted by schinb64 View Post
    Define f: (-1,1) -> R by f(x) = x+1/x^2-1. Does f have a limit at 1? Justify

    I believe that there is no Limit at 1 their is an
    That is corret, the function has no limit at one.

    Look below. (I show that if it does have a limit at one then it implies it is defined on some open interval containing 1 except possible at 1 itself).
    Attached Thumbnails Attached Thumbnails limit problem-picture14.gif  
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