Question

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

• A. ${lim}_{x\to 0+}f\left(x\right)=e$
• B. ${lim}_{x\to 0-}f\left(x\right)=e^2$
• C. f (x) is discontinuous at x = 0
• D. None of these

Answer 1

The correct option is B ${lim}_{x\to 0-}f\left(x\right)=e^2$

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