Introduction to Limits · Superchallenge problem

Complete a table for $g(x)=(\cos x)^{1/x^{2}}$ at $x=\pm0.1,\ \pm0.05,\ \pm0.01$ (radians) and estimate $\displaystyle\lim_{x\to0}(\cos x)^{1/x^{2}}$ to three decimal places. Then, by analyzing $\dfrac{\ln(\cos x)}{x^{2}}$, identify the exact value of the limit as a power of $e$.