Question on limit: $\lim_{x\to 0}\large \frac{\sin^2{x^{2}}}{x^{2}}$ How would I solve the following trig equations?
$$\lim_{x\to 0}\frac{\sin^2{x^{2}}}{x^{2}}$$
I am thinking the limit would be zero but I am not sure.

We use $$\sin^2 x =\frac{1-\cos 2x}{2}$$
$$\lim_{x\to 0}\frac{\sin^2 x^2}{x^2}.=\lim_{x\to 0} \frac {1-\cos 2x^2}{2x^2}=0  $$
