is $\exp \left( - 1 \over x^2 \right ) $ differentiate at $x=0$. Wolframlapha says it is. But is it continuous since we have $1 \over x^2$ and $x=0$? Can we really do this $f(0) = \exp \left( - {1 \over 0} \right)$? I hope I'm making any sense.
EDIT:: Does differentiability necessitate continuity? Is above function continuous at $x=0$.
Also a function $f(x) = {|x| \over x}$ also seems to be differentiable at $x=0$ as mentioned below in comment.