First slide

Introduction to limits

Question

$lim_{x \to 0} \frac{\int_{0}^{x} t \sin (10 t) d t}{x}$ is equal to

Moderate

A

1
B

$10$
C

5
D

0

Solution

$lim_{x \to 0} \frac{\int_{0}^{x} t \sin (10 t) d t}{x}$
$= lim_{x \to 0} \frac{x \sin (10 x)}{1}$ [Using $L'$ Hospital's rule]
$= lim_{x \to 0} x \sin 10 x = 0$

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