For the function

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

For the function f(x)={e1/x−1e1/x+1,x≠00,x=0f(x)=\begin{cases}\frac{e^{1/x}-1}{e^{1/x}+1},&x\ne0\\0,&x=0\end{cases}, which of the following is correct? (a) lim⁡x→0f(x)\lim_{x\to0}f(x) does not exist. (b) f(x)f(x) is continuous at x=0x=0. (c) lim⁡x→0f(x)=1\lim_{x\to0}f(x)=1. (d) lim⁡x→0f(x)\lim_{x\to0}f(x) exists, but f(x)f(x) is not continuous at x=0x=0.

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