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Numerade Educator

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Problem 18 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.

$ \displaystyle \lim_{\theta \to \pi} \frac{1 + \cos \theta}{1 - \cos \theta} $

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Video Transcript

So here we have one plus co sign Tha Tha uh divided by yeah 1- Coastline Data. So we know that code sign pi equals negative one. And we're trying to find the limit as X. Goes to pie or a state it goes to pie. So we see in this case we would get coastline of pie and co sign of pie I would just give us zero. So we don't even have to use the hotel's role in this case. So it's not necessary. In fact we shouldn't because we don't have an indeterminate form. So based on this we can just plug in pi and we will get zero as the final answer. In other cases we might get in a determinant form such as this. Um in which case we would use the hotel's role but it's not necessary to use it here. Because when we take the limit as data goes to pi we end up getting zero as our final answer. So that will be our final answer in this case.