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Math Help - show its continuity

  1. #1
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    show its continuity

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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi

    For the continuity of f, we know that \lim_{h\to0}f(x_0+h)=f(x_0) and we want \forall y\in\mathbb{R},\, \lim_{h\to0}f(y+h)=f(y). You may try to write \lim_{h\to 0}f(y+h)=\lim_{h\to0} f(y-x_0+x_0+h)=\ldots

    For the second question, I suggest you first show that \forall n\in\mathbb{Z}, f(n)=nf(1). Then, you'll be able to show that \forall r\in\mathbb{Q}, f(r)=rf(1). As \mathbb{Q} is a dense subset of \mathbb{R} and f is continuous, you'll be able to generalize the result to the real numbers.

    Why don't you post text instead of images ? Images are annoying because one can't quote the question he is answering...
    Last edited by flyingsquirrel; May 17th 2008 at 01:22 PM.
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  3. #3
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    See this and this.
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