Problem

Find the limit. Use l'Hospital's Rule where appro…

08:19

Problem 7 Easy Difficulty

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. If l'Hospital's Rule doesn't apply, explain why.
$\lim _{x \rightarrow \infty} \frac{\ln x}{\sqrt{x}}$

Answer

$\lim _{x \rightarrow \infty} \frac{2}{\sqrt{x}}=\frac{2}{\sqrt{\infty}}=0$

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Calculus 1 / AB

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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

Okay, so here we have the limit as X approaches infinity of the natural log of X over the square root of X. So we're going to evaluate the limit. And that would be the national lot of infinity over the square root of infinity. And this is gonna be infinity over infinity. So that means we can apply low petals rule eso. This limit then, is going to be equivalent to the limit as X approaches infinity of So take the derivative of Ellen X, which is one over X and then the derivative of the square root of ax, which is going to be 1/2. I guess we won over two times the square root of ax. Okay, we can simplify that. So that's gonna be the you limit as X approaches infinity of two times the square root of X over acts. And we can actually simplify that one step further. When we take squared of X, divided by axe, that is really the same as the limit as X approaches Infinity of two over the square root of ax. I guess I'm not working with this one. We can again evaluate the limit, So we evaluate it, then set it equal to two over the square root of infinity. Okay, well, this is going to be equal to zero. Right? Two divided by larger and larger and larger numbers until the end of time means that it approaches zero. So the limit here is zero.

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