Question

If $f\left(x\right)=\{x\sin \frac{1}{x},x\ne 0k,x=0\}$ is continuous at $x=0$, then the value of $k$ is

• A. $1$
• B. $-1$
• C. $0$
• D. $2$

Answer 1

The correct option is C $0$

If function $f\left(x\right)$ is continuous at $x=0$, then

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

Given, $f\left(0\right)=k$

$\therefore f\left(0\right)=k=\underset{x\to 0}{lim}x\sin \frac{1}{x}$

$\Rightarrow k=0(\because -1\le \sin \frac{1}{x}\le 1)$