Question

Let $f\left(x\right)={\int }_1^x\frac{\sin t}{t}dt$, $\underset{x\to \infty }{\lim }f\text{'}\left(x\right)=$

• A. $0$
• B. $1$
• C. $2$
• D. None of these

Answer 1

The correct option is A

$0$

Explanation for the correct answer.

Given: The function as $f\left(x\right)={\int }_1^x\frac{\sin t}{t}dt$.

Firstly find $f\text{'}\left(x\right)$ we get,

$\begin{array}{rcl}f\text{'}\left(x\right)& =& 1·\frac{\sin x}{x}-0·\frac{\sin 0}{0}\\ & =& \frac{\sin x}{x}\\ & =& 0\end{array}$

Now to find the value of $\underset{x\to \infty }{\lim }f\text{'}\left(x\right)$ we get,

$\underset{x\to \infty }{\lim }f\text{'}\left(x\right)=0$

Therefore, the value of $\underset{x\to \infty }{\lim }f\text{'}\left(x\right)$ is $0$.

Hence, the correct option is (A).