Calculate the Taylor series at x=0 of:

f(x) = exp(-1/x) for x>0; 0 for x\(\leq\)0.

Why is the result interesting?

The part that i am struggling is with is how to approach the problem being that it is a piecewise function. I have calculated the derivatives of the function at x=0. Turns out that they are all undefined for x>0 and 0 for x\(\leq\) 0.

I hope someone will be able to point me in the right direction. Thanks in advance.