Question

find the following limit. notes: enter \dne\ if limit does not exist. $lim_{x
ightarrow0^{+}}lnleft(\frac{6}{x^{3}}
ight)=$

Explanation:

Step1: Analyze the inner - function

As $x
ightarrow0^{+}$, we consider the behavior of $\frac{6}{x^{3}}$. When $x$ approaches $0$ from the right ($x>0$), $\frac{6}{x^{3}}
ightarrow+\infty$.

Step2: Analyze the outer - function

The natural logarithm function $y = \ln(t)$ is a continuous function for $t>0$. When $t
ightarrow+\infty$, $\lim_{t
ightarrow+\infty}\ln(t)=+\infty$. Since as $x
ightarrow0^{+}$, $t = \frac{6}{x^{3}}
ightarrow+\infty$, we have $\lim_{x
ightarrow0^{+}}\ln(\frac{6}{x^{3}})=+\infty$.

Answer:

$+\infty$