Solve the following
Question:

$\lim _{x \rightarrow 0} \int_{0}^{x} \frac{t \sin (10 t) d t}{x}$ is equal to:

  1. (1) 0

  2. (2) $\frac{1}{10}$

  3. (3) $-\frac{1}{5}$

  4. (4) $-\frac{1}{10}$


Correct Option: 1

Solution:

Using L’ Hospital rule,

$\lim _{x \rightarrow 0} \frac{x \sin (10 x)}{1}=0$

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