Find the following limit if it exists: $\lim \ln ( x - 3 )$. Use $\pm \infty$ when appropriate.
$$x \rightarrow 3 ^ { + }$$
A) $\infty$
B) 3
C) 1
D) $- \infty$
E) does not exist

Question

Quizplus · Accepted Answer

As $x$ approaches $3$ from the right, $x-3$ becomes positive but arbitrarily close to $0$. Since $\ln x$ approaches $-\infty$ as $x$ approaches $0$ from the right, $\ln(x-3)$ approaches $-\infty$ as $x$ approaches $3$ from the right. Therefore, the limit does not exist.

Find the Following Limit If It Exists lim⁡ln⁡(x−3)\lim \ln ( x - 3 )limln(x−3)

Find the Following Limit If It Exists $\lim \ln ( x - 3 )$