For the function

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

For the function

f(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\to0}f(x)

does not exist. (b)

f(x)

is continuous at

x=0

. (c)

\lim_{x\to0}f(x)=1

. (d)

\lim_{x\to0}f(x)

exists but

f(x)

is not continuous at

x=0