Find the limit.
-$\lim _ { x \rightarrow 0 ^ { + } } x ^ { 8 } \ln x$
A) 8
B) -1
C) 1
D) 0

Name: Find the limit. -$\lim _ { x \rightarrow 0 ^ { + } } x ^ { 8 } \ln x$ A) 8 B) -1 C) 1 D) 0
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Question

Quizplus · Accepted Answer

We use L'Hospital's rule:
\begin{align*} \lim_{xightarrow 0^+} x^8\ln x &= \lim_{xightarrow 0^+} \frac{\ln x}{1/x^8} \ &= \lim_{xightarrow 0^+} \frac{1/x}{-8/x^9} \
&= \lim_{xightarrow 0^+} -\frac{x^8}{8} \
&= 0 \end{align*}
Therefore, the answer is Choice D, 0.

Find the Limit lim⁡x→0+x8ln⁡x\lim _ { x \rightarrow 0 ^ { + } } x ^ { 8 } \ln xlimx→0+​x8lnx

Find the Limit $\lim _ { x \rightarrow 0 ^ { + } } x ^ { 8 } \ln x$