Problem

The first appearance in print of $1^{\prime}$ Hos…

Problem 56 Medium Difficulty

Prove that
$$\quad \lim _{x \rightarrow \infty} \frac{\ln x}{x^{p}}=0$$
for any number $p>0 .$ This shows that the logarithmic function approaches infinity more slowly than any power of $x .$

Answer

$\lim _{x \rightarrow \infty} \frac{\ln x}{x^{p}}=0$

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Chapter 4

Applications of Derivatives

Section 3

L'Hospital's Rule: Comparing Rates of Growth

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Video Transcript

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