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Math Help - Proving Continuity

  1. #1
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    Proving Continuity

    Greetings all,

    I am not sure which theorem to use to answer this question. It says to not use the Delta/E definition of limit and prove that this function is continuous when x=0. I think the theorem to use is the intermediate value theorem.

    the function is g(x)= {x2cos (1/x) when x does not equal 0
    and the other is {0 when x=0
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  2. #2
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    Re: Proving Continuity

    Quote Originally Posted by funnybabe View Post
    the function is g(x)= {x2cos (1/x) when x does not equal 0
    and the other is {0 when x=0
    \left| {x^2 \cos \left( {\frac{1}{x}} \right) - 0} \right| \leqslant \left| {x^2 } \right|.
    Think about \delta=\sqrt{\varepsilon }
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