First slide

Introduction to limits

Question

$lim_{x \to 0} \frac{(1 - \cos 2 x) \sin 5 x}{x^{2} \sin 3 x}$ equals

Moderate

A

$\frac{10}{3}$
B

$\frac{3}{10}$
C

$\frac{6}{5}$
D

$\frac{5}{6}$

Solution

We have,
$\begin{array}{l} lim_{x \to 0} \frac{(1 - \cos 2 x) \sin 5 x}{x^{2} \sin 3 x} \\ = lim_{x \to 0} 2 {(\frac{\sin x}{x})}^{2} \times (\frac{\sin 5 x}{5 x}) \times \frac{5 x}{3 x} \times (\frac{3 x}{\sin 3 x}) = \frac{10}{3} \end{array}$

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