Evaluating Limit - $(1-\cos(x^2))/(x^3\sin(x))$ How would you go about evaluating the following limit as $x$ approaches $0$?
$$\lim_{x\to 0}\frac{1-\cos(x^2)}{x^3\sin(x)}$$

$$\frac{1-\cos(x^2)}{x^3\sin(x)}=\frac{2\sin^2\left(\frac{x^2}{2}\right)}{x^3\sin(x)}=\frac{1}{2}\left(\frac{\sin\left(\frac{x^2}{2}\right)}{\frac{x^2}{2}}\right)^2\frac{x}{\sin(x)}$$
then use $\displaystyle \lim_{x\to 0}\frac{x}{\sin(x)}=1$, you get your result.
