TITLE: Continuous function with constant
QUESTION [0 upvotes]: There is function $f(x)=e^{(c^2 - 1)/x^2}$ when $x \neq 0$ and $f(x)=c$ when $x=0$.
Why is this function continuous (the $c$ is a constant)? 
I know that for the function to be continuous, $\lim_{x\to c}f(x)=f(c)$
but I'm not sure where to start

REPLY [2 votes]: Hint:
note that, for $c^2-1=a$ we have:
$$
\lim _{x \to 0}\;e^{\frac{a}{x^2}}= \begin {cases}
=0 \quad \mbox{for} \quad a<0\\
=+\infty\quad \mbox{for} \quad a>0
\end{cases}
$$
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