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Math Help - Proof that Limits doesn't exist - Help...

  1. #1
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    Proof that Limits doesn't exist - Help...

    My friend, who doesn't have access to the internet right now, needs help with this question...

    Prove, using the precise definition, that lim x->5 \frac {1} {x - 5} does not exist
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    Well there are many precise definitions.

    Let f(x)=\frac{5}{x-5}. Suppose \{x_n\} is a sequence of positive real numbers tending to 0. Then \{5-x_n\} and \{5+x_n\} both tend to 5 but \{f(5-x_n)\} tends to -\infty while \{f(5+x_n)\} tends to +\infty. Therefore the limit does not exist.
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