Let for , and let .…

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

Problem

Let

f(x)=\left(1+\frac{1}{x}\right)^x

for

x>0

, and let

g(x)=\begin{cases}x\ln\left(1+\frac{1}{x}\right),&0<x\le1\\0,&x=0\end{cases}

. Then

\lim_{x\to0^+}g(x)

(1) is equal to

0

(2) is equal to

1

(3) is equal to

e

(4) does not exist