Calculating Residuals for Singularities in Complex Functions

[Tosh5457]

Homework Statement

Calculate the residuals of the following functions in the corresponding singularities:
1) $$f(z) = z^{2}\exp (\frac{1}{z})$$
2) $$f(z) = exp(\frac{-1}{z^{2}})$$

Homework Equations

The Attempt at a Solution

I can't tell if these functions have poles or not, because I can't calculate $$lim z \to 0 (z^{m}f(z))$$, for any natural m. Is it even possible to calculate the residuals this way, or do i need to put the function in Laurent series (which I haven't studied yet)?

 

[susskind_leon]

Try expressing the exponential by its taylor series.