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Problem

Find the limit. Use l'Hospital's Rule where appro…

01:17

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Problem 8 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 3} \frac{x - 3}{x^2 - 9} $


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02:41

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Mengsha Yao

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

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Watch More Solved Questions in Chapter 4

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Problem 9
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Problem 16
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Problem 82
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Problem 89
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Problem 91
Problem 92

Video Transcript

So this problem here is going to have two different methods. We know that our graph is going to be X -3 divided by x squared minus nine. But remember the x squared minus nine can be written as X plus three times x minus three. Based on this, we see that the X -3 is will cancel just giving us one over X plus three. So based on this, we see that when we just plug in a three we'll get 1/6 as our limit. So 1/6 is our limit. Um That will be the answer. We can also use little cows rule though, because as we saw before, if we plugged in right here, if we plugged in a three, we would get 0/0, which would be the indeterminant form based on that. We can use locales rule to give us Um when we took the driver of this, we get one and we take the derivative of this, we would get to X based on that when we plug in a three, then once again it'll be 1/2 times three. So that would give us 1/6 as the final answer. So you see in two cases we'll get 1/6. Oftentimes there won't be that first option, but it is nice to be able to see it because it's easier not to have to take the derivative if you don't have to, it's easier to recognize that we can just factor and then um cancel the numerator and denominator and then evaluate the limits. Okay?

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Related Topics

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Video Thumbnail

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Video Thumbnail

06:14

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A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

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