Question

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

• A. $1$
• B. $0$
• C. $-1$
• D. Indeterminate

Answer 1

The correct option is B $0$

$f\left(0\right)=\underset{x\to 0}{lim}x\sin \frac{1}{x}$
We know $\forall x\in R,\sin \frac{1}{x}\in [-1,1]$
Hence, $f\left(0\right)=\underset{x\to 0}{lim}x\sin \frac{1}{x}=0$