Limit with parameter, $(e^{-1/x^2})/x^a$ How do I explore for which values of the parameter $a$
$$ \lim_{x\to 0} \frac{1}{x^a} e^{-1/x^2} = 0?
 $$
For $a=0$ it is true, but I don't know what other values.

Hint: You may rewrite the equation
$$ \frac{1}{x^a} e^{\frac{-1}{x^2}} = \frac{1}{x^a e^{\frac{1}{x^2}}} = \frac{1}{e^{a \ln(x)+ \frac{1}{x^2}}}$$
