Question

If $f\left(x\right)=\{\begin{array}{cc}si{n}^{-1}|x|,& whenx\ne 0\\ 0,& whenx=0\end{array}$ 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

${lim}_{x\to 0}f\left(x\right)=si{n}^{-1}\left(0\right)=0$ and f(0) = 0
Hence f(x)is continuous at x = 0