Question

If $f\left(x\right)=\{\begin{array}{cc}{2}^{\frac{1}{x}},& forx\ne 0,\\ 3,& forx=0\end{array}$, then

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

Answer 1

The correct option is D None of these

${lim}_{x\to 0+}f\left(x\right)={lim}_{k\to 0}{2}^{\frac{1}{k}}=\infty$
${lim}_{x\to 0-}f\left(x\right)={lim}_{k\to 0}{2}^{\frac{-1}{k}}={lim}_{k\to 0}\frac{1}{2^{\frac{1}{k}}}=0$