Question: $\lim _{x \rightarrow 0} \int_{0}^{x} \frac{t \sin (10 t) d t}{x}$ is equal to:
(1) 0
(2) $\frac{1}{10}$
(3) $-\frac{1}{5}$
(4) $-\frac{1}{10}$
Correct Option: 1
Solution:
Using L' Hospital rule,
$\lim _{x \rightarrow 0} \frac{x \sin (10 x)}{1}=0$
