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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

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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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