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Numerade Educator

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Problem 50 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.

$ \displaystyle \lim_{x\to (\pi/2)^-} \cos x \sec 5x $

Answer

$\frac{1}{5}$

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Video Transcript

So we want to use little zero in order to find the limit of this function. And the easiest way to think about this rather than using co sign and seek. It would be the coastline of X. Divided by because sine of phi bets. And we see that when we plug in pi over two we're just going to get 0/0. But if we use low petals rule what we end up getting in. The numerator is a negative sign. It's and then what we get in the denominator is a negative five sign five X. Now when we plug in however to we'll end up getting a one up here and then because the negatives are going to cancel so we'll get one over five times sine of pirate too. So as a result of that, that's just me. 1/5. Uh so 1/5 will be our final answer in using what Charles Rule.