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Thread: sided limit

  1. #1
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    sided limit

    I have to show $\displaystyle \lim_{x\to 1^+}\frac{x}{x-1}=+\infty$
    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 $\displaystyle \lim_{x\to 1^+}\frac{x}{x-1}=+\infty$
    I have no idea how to begin... any help?
    $\displaystyle \frac{x}{x-1}=1+\frac{1}{x-1}$ So you want to prove that $\displaystyle \forall N$, $\displaystyle \exists~\delta>0$ such that $\displaystyle |x-1|<\delta$ implies $\displaystyle 1+\frac{1}{x-1}>N$.

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