Chapter 2 - Derivatives - 2.4 Derivatives of Trigonometric Functions - 2.4 Exercises - Page 151: 48

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Given $$\lim _{x\to 0}\frac{\sin x^2}{x}$$ Then \begin{align*} \lim _{x\to 0}\frac{\sin x^2}{x}&=\lim _{x\to 0}\frac{x\sin x^2}{x^2}\\ &=\lim _{x\to 0}(x)\lim _{x \to 0}\frac{ \sin x^2}{x^2}\\ &=\lim _{x\to 0}(x)\left(\lim _{x \to 0}\frac{ \sin x }{x }\right)^2\\ &=(0)(1)\\ &=0 \end{align*}