Question

$\underset{x\to 0}{\lim }\frac{3{\sin }^{2}x-2\sin x^2}{3x^2}$

Answer 1

$$\begin{gathered} \underset{x\to 0}{\lim }\left[\frac{3{\sin }^{2}x-2\sin x^2}{3x^2}\right] \\ =\underset{x\to 0}{\lim }\left[\frac{3{\sin }^{2}x}{3x^2}-\frac{2\sin x^2}{3x^2}\right] \\ =1-\frac{2}{3} \\ =\frac{1}{3} \end{gathered}$$