Chapter 2 - Derivatives - 2.4 Derivatives of Trigonometric Functions - 2.4 Exercises - Page 151: 44

$15$

Given $$\lim_{x\to 0}\frac{\sin 3x\sin 5x}{x^2} $$ Then \begin{align*} \lim_{x\to 0}\frac{\sin 3x\sin 5x}{x^2}&=\lim_{x\to 0}\frac{\sin 3x\sin 5x}{x\cdot x}\\ &=\lim_{x\to 0}\frac{\sin 3x}{x}\frac{\sin 5x}{ x}\\ &=15\lim_{3x\to 0}\frac{\sin 3x}{3x}\lim_{5x\to 0}\frac{\sin 5x}{5 x}\\ &=15 \end{align*}