Download the App!

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

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

Use the guidelines of this section to sketch the …

04:48

Question

Answered step-by-step

Problem 68 Hard Difficulty

Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote.

$ y = \dfrac{x^3}{(x + 1)^2} $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Jamie M
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Jamie M

Numerade Educator

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

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 5

Summary of Curve Sketching

Related Topics

Derivatives

Differentiation

Volume

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Grace He
Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Kristen Karbon

University of Michigan - Ann Arbor

Calculus 2 / BC Courses

Lectures

Video Thumbnail

04:35

Volume - Intro

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.

Video Thumbnail

06:14

Review

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.

Join Course
Recommended Videos

03:14

Use the guidelines of this…

02:43

Use the guidelines of this…

01:31

Use the guidelines of this…

03:11

Use the guidelines of this…

02:15

Use the guidelines of this…

03:50

Use the guidelines of this…

04:30

Use the guidelines of this…

0:00

Use the guidelines of this…

04:59

Use the guidelines of this…

Watch More Solved Questions in Chapter 4

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76

Video Transcript

here we have domain cannot be won and it cannot be won. No, a negative one cannot be negative one because the denominator cannot be zero intercept. 00 There's no symmetry. But we do have asking. Tooks, you have an s in tow. Er we have vertical one. Andy, Slant one. Now the vertical is the easier one to find. The denominator said equal to zero X equals negative. One is a vertical for our slant as Anto consult for it by doing polynomial division. All right, I'll spoil this out. So we have X squared close to X plus one. Okay, here we have X squared into X cute X X Times X squared would normally be X cubed, but we're going to change the sign to cancel the first term. Okay, so the first term cancels x times, times two ex sort of the sign minus two x squared. Next time one's is going to be. And then there was with the sine minus X. Okay. And now we have, um, ex weird in tow, minus two x squared. So minus two minus two times. Um X weird. Bring this down minus two times x squared. But switched the sign positive to next spared. And now negative. Two times two x would be minus for X. But we have to search a sign so positive for X. All right. And then positive two. Okay. And received. This cancels out, and the next term would have in mind would be the ex, but, um, X squared has a higher power than X. So we're done in their division. We'd, uh, remainder, obviously. But this is the important part that we need right now. X minus two is our slam doesn't. And now we can look a, um, boy prime. Why? Prime is X squared times X plus three over X plus one cubed. Set that equal to zero. I'm gonna need a bigger line in that and we get X equals zero. An X equals negative three. Facilitate. This is F prime. Well, then get it. Three. Now, let's say that zero. And remember, we have asked in tow X equals negative one. So let's just say it's right there. All right, so it's gonna be an increasing interval year decreasing here and then increasing here in here, making this a maximum value local maximum value f of negative. Three is going to be approximately negative. 6.75. That's it for the first derivative test. And now we can look at Kong cavity with the second derivative test. I need to make that a little smaller. Okay, so the second derivative test, Why double print this six X over explosive? One to the fourth said it equal to zero, and we get X equals zero. Put that on her first derivative, second derivative test zero. And we see that it's Kong cave down here. Concave up here, making this an inflection point. Okay, so that's it for Colin Cavity. I made this really small because this craft is going to take up. Look, some space. All right, let's make some room. All right. What has our original functions? Move that over here. I'll Circle and Ritter are in blue. Are original function to make more room for the Griff. Mostly gonna be down here, so all right, We haven't intercepted 00 next weekend. Put our ascent oats at negative one X's negative one. And we have a slant. Wonder why equals X minus two. So if we see that this is too 12 and This is one, too. Then we have a slant, as in two going through here, or it's. And now we know that we have the minimum negative. Three negative. 6.75. So let's just say this is negative. Three negative. 6.75. And we know it's gonna be like this because it is a local maximum. It has the curvature to it. Difficult to draw. But there's a curve. All right. Okay. And next we have our Now, how does the graph approach or intercept? Well, we know that it's going to be con cave down before it reaches zero. So it's gonna be down, down, down, approaching, but never touching the ass in tow. And then it's going to come to zero, and then it's gonna become keep up the rest of the way and approach, but never touch our ass in tow.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
192
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
83
Hosted by: Alonso M
See More

Related Topics

Derivatives

Differentiation

Volume

Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Kristen Karbon

University of Michigan - Ann Arbor

Calculus 2 / BC Courses

Lectures

Video Thumbnail

04:35

Volume - Intro

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.

Video Thumbnail

06:14

Review

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.

Join Course
Recommended Videos

03:14

Use the guidelines of this section to sketch the curve. In guideline $D$ find a…

02:43

Use the guidelines of this section to sketch the curve. In guideline $D$ find a…

01:31

Use the guidelines of this section to sketch the curve. In guideline D find an …

03:11

Use the guidelines of this section to sketch the curve. In guideline $D$ find a…

02:15

Use the guidelines of this section to sketch the curve . In guideline D find an…

03:50

Use the guidelines of this section to sketch the curve. In guideline $D$ find a…

04:30

Use the guidelines of this section to sketch the curve. In guideline D find an …

0:00

Use the guidelines of this section to sketch the curve. In guideline $\mathrm{D…

04:59

Use the guidelines of this section to sketch the curve. In guideline D find an …
Additional Mathematics Questions

01:32

a girl shaded two - thirds of half of a circle. which type of circle shows t…

01:48

A game consists of tossing a one-rupee coin 3 times and noting its outcome e…

02:03

a box of colouring sketch pens costs 98 of have 600 then what is the maximum…

02:03

a box of colouring sketch pens costs 98 of have 600 then what is the maximum…

02:10

a large number of measurement is normally distributed with mean of 65.5 cm a…

01:05

In ABC School, students are evaluated on the basis of an exam which they con…

02:17

in a survey of 150 high school students it was found that 18 students have l…

01:14

Combining method packages from any of the three layers of the method reposit…

00:33

Write coefficient of x^2 in x^4 +7x^3 + 9x^2 + 11

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started