Question

Discuss the continuity of $0\le x\le 1$ & differentiability at $x=0$ for the function $f\left(x\right)=x.\sin x$

Answer 1

$f\left(x\right)=x.\sin x$

${lim}_{x\to 0^{-}}f\left(x\right)={lim}_{x\to 0^{+}}f\left(x\right)=f\left(0\right)=0$

It is continuous at $x=0$