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Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example $2,$ change the denominator $5 x$ to $5 \ln x$

$\infty$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 7

L'Hospital's Rule

Derivatives

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Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

01:02

Express as a single logari…

00:44

Rewrite the expressions in…

00:59

Convert the following expr…

00:32

Use the Laws of Logarithms…

00:47

Changing bases Convert the…

00:29

Write each equation as an …

Apply the properties of lo…

01:13

Solve each equation.

00:33

Solve each equation. See E…

Use properties of logarith…

All right. We are redoing this problem. The limit as X goes to infinity of the numerator stays the same three E. To the two X. But we're rewriting the denominator as five natural log of X. Yeah. So in this problem, if we were to think about what happens for both these functions they eat to the two X. Uh as we're going, that's what that graph looks like. So alright. And for numerator and the five natural log effect looks like this. That's the denominator. So they are both going infinitely. Uh So we do have we still have the indeterminate form of infinity over infinity to do low petals rule. So what we need to do is take the derivative of the top. So it's going to be equal to the limit limits the same thing. But the derivative of the top of the 6E. to the uh two X. That's using the Chambal. And the derivative of the bottom of the five divided by X. The derivative of natural log is one of rex. So that's now equal to the limit as X goes to infinity of well six fists. But when you're dividing by the X and the denominator, think about multiplying by the reciprocal. So it's going to go into the numerator X. E. To the two X. Um So in this case the derivative is going infinitely up. Um but I think it would be safe to say because in order for a limit to exist, it needs to equal numerical value. So we usually just use this phrase. The limit does not exist. DNA means does not exist.

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