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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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01:38
Wen Zheng
01:14
Amrita Bhasin
Calculus 1 / AB
Calculus 2 / BC
Chapter 4
Applications of Differentiation
Section 4
Indeterminate Forms and l'Hospital's Rule
Derivatives
Differentiation
Volume
Baylor University
University of Nottingham
Idaho State University
Boston College
Lectures
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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.
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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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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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