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Math Help - limit of 1/(x-1)

  1. #1
    jbd
    jbd is offline
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    limit of 1/(x-1)

    Hi, is it possible to evaluate 1/(x-1) at x=1 by any means?

    Thanks
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  2. #2
    MHF Contributor

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    As x gets closer and closer to 1, the numerator remains 1 while the denominator gets closer and closer to 0- the entire fraction (in absolute value) gets larger and larger- there is NO limit.

    You can't even say " \displaytype\lim_{x\to 1}\frac{1}{x- 1}= \infty".

    If x< 1, the denominator is negative so \displaytype\lim_{x\to 1^-}\frac{1}{x- 1}= -\infty.

    If x> 1, the denominator is positive so \displaytype\lim_{x\to 1^+}\frac{1}{x- 1}= \infty.
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