💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!



Numerade Educator



Problem 74 Hard Difficulty

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


$\lim _{x \rightarrow \infty} \frac{1}{p x^{p}}=\frac{1}{\infty}=0$

More Answers


You must be signed in to discuss.

Video Transcript

Okay, we know we have indeterminant form insanity over infinity, implying we have to use law. Attwell's rule. Okay, let's take the derivative of the top derivative of natural Have access simply one of racks. Derivative of extra p is P which is the coefficient of the experiment p x to the P minus one. You have the limit as X approaches infinity off one over p x, the p. It's the same thing as one over infinity, which is simply zero.