Problem

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

06:19

Problem 9 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.
$\lim _{x \rightarrow 0^{+}} \frac{\ln x}{x}$

Answer

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Calculus 1 / AB

Biocalculus Calculus for the Life Sciences

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 natural log of X over Rex, and we want to find the limit as X approaches zero of it. No, Normally, we would try to solve, put zero in until we get. But of course, that's gonna be undefined both at the top and the bottom eso lo kettles. Rule doesn't actually really work here in that case, so we're going to consider instead is but the limit as X approaches zero the central of ex multiplied by the limit as X approaches zero of one over X. Okay, now the limit. Yeah, of this right portion here. But this is gonna be equal to 1/0, which is, of course, infinity. And then this one, the luck portion the limit as experts zero from the right hand side of the natural log of X is going to be negative. Infinity. It says the property. That's good to know. The graph of the natural log of X looks something like this. Right? So at zero, it's going to be negative. Infinity. And so we multiply that together. We're getting the limit as X approaches zero. The natural light of eggs over X is going to be equal to negative infinity. Multiply it by infinity. It was just really negative. Infinity squared. But that's Sonia. What? That's gonna be negative. Infinity. So the solution here is negative Infinity!

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