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Math Help - need confirmation of counterexample

  1. #1
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    need confirmation of counterexample

    Hi! I have to find a counterexample to the following statement:
    \lim_{x\to \infty}f(\frac{1}{x})=L implies \lim_{x\to 0}f(x)=L

    I assert that f(x)=\left\{\begin{array}{lr}1:&x>0\\-1:&x\leq 0\end{array}\right\} is a viable counterexample.

    Is this correct?
    The limit at 0 does not exist, but the limit of f(x) as x goes to infinity will be 1.
    Im just not 100% sure...
    Any feedback would be appreciated.
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  2. #2
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    Quote Originally Posted by dannyboycurtis View Post
    Hi! I have to find a counterexample to the following statement:
    \lim_{x\to \infty}f(\frac{1}{x})=L implies \lim_{x\to 0}f(x)=L

    I assert that f(x)=\left\{\begin{array}{lr}1:&x>0\\-1:&x\leq 0\end{array}\right\} is a viable counterexample.

    Is this correct?
    The limit at 0 does not exist, but the limit of f(x) as x goes to infinity will be 1.
    Im just not 100% sure...
    Any feedback would be appreciated.

    Nice, simple and neat example...oh, and correct, too.

    Tonio
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