Download the App!

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

Question

Answered step-by-step

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 0} \frac{\cos mx - \cos nx}{x^2} $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Carson Merrill

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

03:05

Mengsha Yao

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

Derivatives

Differentiation

Volume

Campbell University

University of Michigan - Ann Arbor

Idaho State University

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.

08:58

Find the limit. Use l'…

01:13

02:49

01:36

Find the limit. Use I'…

07:50

01:18

01:37

01:02

03:38

01:16

01:00

04:03

00:53

09:21

So for this problem we're gonna be using reptiles rule. Um in order to find the limit as X approaches zero, the function. So in this case what we have is coastline mx minus coastline. An X over X squared. And because it's zero, we know that that's going to give us 0/0. Which is the indeterminant form. So when we take the derivative of the top and the bottom we'll end up getting is a negative mm sign mx plus and sign nx All divided by two x. Then we would still get the indeterminate form. When we evaluated at X equals zero, we would just get 0/0 again. So we have to take the derivative one more time. That's gonna end up giving us uh negative M squared. Uh Co sign annex plus and squared could sign mhm. An axe that's going to end up giving us um just M squared negative M squared plus M squared As a result when we plug in zero. And this is just going to become, too when we took the derivative. So our final answer is going to be n squared minus m squared or negative m squared plus n squared over to um and that will be the final value of the limit. So this problem shows that even if we don't have specific values, we can still evaluate limits um depending on circumstances.

View More Answers From This Book

Find Another Textbook

01:23

Iruediua Ilue_Tlcor Several delective thermometers being tested by the compa…

03:09

point) Identify the type of quadric surface defined by the equation2x

01:31

11Construct a frequency distribution for this data using 5 classes Using…

04:52

Solve the initial value problem _9y' _ 4y = e #, Y(0) =a Let @o be …

05:25

ChapterCheck the BasicsCHECK THE BASICS For Exercise 31. puge 47; …

02:00

State whether the data described below are discrete or continuous and explai…

02:03

Suppose we select random of size forty recently issued building permits for …

02:17

8. [16/20 Points]DETAILSPREVIOUS ANSWERSDEVORESTAT9 2.E.035M…

03:42

For each set of rational numbers in Exercises 9 and 10,draw a number line an…

00:07

(10 points) Determine if each statement is True or False and explain your re…