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Numerade Educator

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Problem 42 Hard 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.

$ \displaystyle \lim_{x\to a^+} \frac{\cos x \ln(x - a)}{\ln(e^x - e^a)} $

Answer

$\cos (a)$

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Video Transcript

Okay. We know that if we have natural of X minus a over natural log of each of the AKs menace, eat of the eh? We end up with negative infinity over negative infinity. Which means we can apply. Well, hoppy tolls rule. Now we still have zero over zero. We can apply the hoppy tolls rule again times one over eat of the A this cancels and we simply end up with co sign of a