First slide

Introduction to limits

Question

$lim_{x \to 0} \frac{(1 - e^{x}) \sin x}{x^{2} + x^{3}}$ is equal to

Moderate

A

$- 1$
B

0
C

1
D

2

Solution

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

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