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Problem 36 Easy Difficulty

Determine the infinite limit.

$ \displaystyle \lim_{x \to 0^+}\ln (\sin x) $

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Video Transcript

to evaluate this limit, we recall finding the limit of the natural log of a certain function. That is, if we have limits as X approaches E of Ln of F of X. This is the same as taking the limit of F of X inside the natural log. That is L. N. Of limit as X approaches A. Of a Fedex. And so from here we can read this as Ln of the limit as X approaches zero from the right of sine X. Now evaluating at zero, we have Ln of sign of zero, which is just zero. And so we have Ellen of zero. And looking at the graph of L innovex, we see that as X gets closer to zero from the right, the value of L. N approaches negative infinity. And so this will be negative infinity. And so this is the value of the limits.