Question

If $f\left(x\right)=\{\begin{array}{cc}\frac{1}{x}sin{x}^2,& x\ne 0\\ 0,& x=0\end{array}$ , then

• A. ${lim}_{x\to 0+}f\left(x\right)\ne 0$
• B. ${lim}_{x\to 0-}f\left(x\right)\ne 0$
• C. f(x) is continuous at x = 0
• D. None of these

Answer 1

The correct option is C f(x) is continuous at x = 0

$f\left(0\right)=0,{lim}_{x\to 0+}f\left(x\right)={lim}_{x\to 0-}f\left(x\right)={lim}_{x\to 0}x\left[\frac{sin{x}^2}{x^2}\right]=0$