First slide

Introduction to limits

Question

$lim_{x \to 0} \frac{\sin x^{n}}{(\sin x)^{m}}, (m < n)$ is equal to

Moderate

A

1
B

0
C

$n / m$
D

none of these

Solution

We have,
$\begin{array}{l} lim_{x \to 0} \frac{\sin x^{n}}{(\sin x)^{m}} \\ = lim_{x \to 0} (\frac{\sin x^{n}}{x^{n}}) (\frac{x^{n}}{x^{m}}) {(\frac{x}{\sin x})}^{m} \\ = lim_{x \to 0} x^{n - m} = 0 \end{array}$

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