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Numerade Educator

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Problem 26 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_{\mu \to 0} \frac{e^{\mu /10}}{u^3} $

Answer

$\infty$

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Video Transcript

So here, what we're given is E to the you over can um it's actually new but we don't have me. So we'll just use the letter U over U. Cubed. And when we plug in infinity we would just get infinity over infinity. Now this is an indeterminate form. So what we want to do is take the derivative of both the top and the bottom. Um So when we do this we end up getting for the derivative of the top. That's going to be Uh one over 100 Times. E should be view over 10. And then on the bottom we'll get three you square now. Again we'll get infinity over infinity. So we want to do this again. This will give us one over 1000 E. To the U. Over 10 and this will give us six you on the bottom. Once again, when we plug in infinity will get in a determinant form. So we'll do it one more time. Um so the initial one should have been won over 10, then one over 100. The last one is going to be one over 1000 with just six in the numerator or the denominator. So as a result of that, we see that still when we plug in um you actually get infinity in the numerator, however, will only get a six and the denominator. So if we get infinity Divided by six, that's going to be just infinity. So our final answer is infinity.