Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

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 \infty} (x - \ln x) $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

The limit has the form $\infty-\infty$ and we will change the form to a product by factoring out $x$\[\lim _{x \rightarrow \infty}(x-\ln x)=\lim _{x \rightarrow \infty} x\left(1-\frac{\ln x}{x}\right)=\infty \text { since } \lim _{x \rightarrow \infty} \frac{\ln x}{x} \stackrel{\Perp}{x}=\lim _{x \rightarrow \infty} \frac{1 / x}{1}=0\]

01:46

Wen Zheng

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

Derivatives

Differentiation

Volume

Oregon State University

Baylor University

University of Nottingham

Boston College

Lectures

04:35

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.

06:14

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.

02:22

Find the limit. Use l'…

06:18

01:56

02:03

01:32

06:16

01:36

01:58

01:17

01:16

00:34

05:23

okay. It's easier to rewrite access. Natural Law defeated the X for the purpose of manipulating it. When we have to apply the hoppy tolls rule you can write. This is e to the X over Max. And then we have the natural walk. Okay, Now we know we end up with the form infinity over infinity. Therefore, we know we must apply the hospital's rule. We end up with the natural log of infinity, which is simply infinity.

View More Answers From This Book

Find Another Textbook

01:19

'Find the remainder 5 2x 3x2 divided iq 7'

02:53

'4_ Formulate and solve: In a school election, Juan received 4 times as…

'A rectangular storage container with an open top is to have volume of …

01:40

'Q2: Among the cight _ graphs below are six graphs that display the fun…

04:33

'13_ A cylindrical can with a closed top is made to contain 150 cm3 of …

02:14

'Salary information regarding male and female employees of a large comp…

01:51

"A patient'$ temperature for five days after surgery taken at 7;00…

02:16

'17) Americans consume approximately averagc of 1.64 cups of coffee per…

03:00

'10. Hypothesis Test for Effect = of Marijuana Use on College Students:…

01:00

'Do poorer people tend to have shorter lives than richer people? Two re…