The limit $\lim _ { x \rightarrow 0 ^ { - } } \ln \left( e ^ { x } - 1 \right)$ is

A) $- \infty$
B) $\infty$
C)-1
D)1
E)0

Question

The limit $\lim _ { x \rightarrow 0 ^ { - } } \ln \left( e ^ { x } - 1 \right)$ is

A) $- \infty$
B) $\infty$
C)-1
D)1
E)0

Quizplus · Accepted Answer

As $x$ approaches 0 from the left, $e^x$ approaches 1. Thus, $e^x - 1$ approaches 0. Since the natural logarithm of a number very close to 0 (but less than 0, since we're approaching from the left and subtracting 1) is negative and approaches $-\infty$, the correct answer is $-\infty$.

The Limit lim⁡x→0−ln⁡(ex−1)\lim _ { x \rightarrow 0 ^ { - } } \ln \left( e ^ { x } - 1 \right)limx→0−​ln(ex−1)

The Limit $\lim _ { x \rightarrow 0 ^ { - } } \ln \left( e ^ { x } - 1 \right)$