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Math Help - limits

  1. #1
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    limits

    Use the definition of a limit epsilon and delta to find the following limit.

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  2. #2
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    Note that in the limit x \ne 0 thus \left| {\sin \left( {\frac{1}{{x^2 }}} \right)} \right| \leqslant 1
    So \left| {x\sin \left( {\frac{1}{{x^2 }}} \right)} \right| \leqslant \left| x \right|.
    Just let \varepsilon  > 0 \Rightarrow \quad \delta  = \varepsilon .
    Now you use the definition.
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