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Problem

Illustrate l'Hospital's Rule by graphing both $ f…

01:22

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Problem 70 Hard Difficulty

Use a graph to estimate the value of the limit. Then use l'Hospital's Rule to find the exact value.

$ \displaystyle \lim_{x\to 0} \frac{5^x - 4^x}{3^x - 2^x} $


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Wen Zheng

01:14

Amrita Bhasin

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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Differentiation

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04:35

Volume - Intro

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

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06:14

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Video Transcript

this problem, we're gonna start by graphing the function that were given. Um and that's Y equals five X -4. The axe. Try to buy 3 to the X -2 D backs and we look at this graph zooming out and we see it looks like this, we want to know the limit as X approaches zero, so we zoom in towards zero and we see it looks like it's approaching while it's undefined, it appears to be approaching some value Around .55, perhaps, maybe Around there. So .55. Um When we take the limit, when we um plug in zero, we see that we get the indeterminant form but we can use locales rule to simplify this and we end up getting the natural log of five minus the natural log of four Over the natural log of 3- the natural log of two. And that's gonna give us .5503. So um we had a good estimation but we did not get it exactly, so that's why it's important just to calculate it

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Top Calculus 2 / BC Educators
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Video Thumbnail

04:35

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In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

Video Thumbnail

06:14

Review

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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