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Math Help - sided limit

  1. #1
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    sided limit

    I have to show \lim_{x\to 1^+}\frac{x}{x-1}=+\infty
    I have no idea how to begin... any help?
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by dannyboycurtis View Post
    I have to show \lim_{x\to 1^+}\frac{x}{x-1}=+\infty
    I have no idea how to begin... any help?
    \frac{x}{x-1}=1+\frac{1}{x-1} So you want to prove that \forall N, \exists~\delta>0 such that |x-1|<\delta implies 1+\frac{1}{x-1}>N.

    So given an N, let \delta=\frac{1}{N-1}.
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