How do I prove that $f(x)=e^x$ is a continuous function at the point $x=0$? I understand that anything raised to the $0$ power equals $1$, therefore it is continuous. But I don't know how to write a proof to show that. Please help.
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Do you have to use the definition of continuity, with $\epsilon$ and $\delta$? You could also show that $lim_{x\rightarrow 0}e^x=1=e^0$. – Marra Sep 08 '13 at 18:54
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Just because $f(0)=1$ doesn't mean it is continuous. What definition are you using for $e^x$? – Owen Sizemore Sep 08 '13 at 19:01
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I'm not sure. I just typed the question exactly how it appears in the book. – redundant01 Sep 08 '13 at 19:50
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Yes, just looked. They want me to use Epsilon Delta definition, not the limit definition. I don't know if I am supposed to pick an epsilon, or or show a delta or what... they gave me some absolute values and I'm not sure what to do with it. – redundant01 Sep 08 '13 at 22:58