Answer
$$A=\lim\limits_{x\to0}\frac{\sin x^2}{x}=0$$
Work Step by Step
$$A=\lim\limits_{x\to0}\frac{\sin x^2}{x}$$ $$A=\lim\limits_{x\to0}\Bigg(\frac{\sin x^2}{x^2}\times x\Bigg)$$ $$A=\lim\limits_{x\to0}\frac{\sin x^2}{x^2}\times\lim\limits_{x\to0} x$$
Let $x^2=\theta$. Then as $x\to0$, $\theta\to0$. So, $$A=\lim\limits_{\theta\to0}\frac{\sin\theta}{\theta}\times\lim\limits_{x\to0} x$$ $$A=1\times0=0$$
