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Numerade Educator

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Problem 38 Medium 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\to 0^+} \frac{x^x - 1}{\ln x + x - 1} $

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Video Transcript

So here we're going to be finding the limit um possibly through using hotels rule, we have to determine that. So we see that in this case we have X to the X. Right, that's one. And since we're approaching zero, that's going to be a potential issue. Um And then we'll have this divided by the natural log of X. Let's act my next one. That's what we're dealing with here. And we want to know the limit as X approaches zero from the right. So in this case we wouldn't really use locals rule instead. What we can do is take the limit as X goes to zero from the right, um and recognize what's happening. So looking at the graph here, we see that as we approach X from the right or as we approach zero from the right, It's constantly approaching a value of zero. So based on that, we see that the answer is going to be zero.