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

Show that the curve $ y = \sqrt{x^2 + 4x} $ has t…

01:49

Question

Answered step-by-step

Problem 71 Hard Difficulty

Show that the curve $ y = x - \tan^{-1} x $ has two slant asymptotes: $ y = x + \pi /2 $ and $ y = x - \pi /2 $. Use this fact to help sketch the curve.


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Bobby Barnes
University of North Texas

Like

Report

Textbook Answer

Official textbook answer

Video by Bobby Barnes

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

Caleb Elmore

Baylor University

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

01:49

Show that the curve $ y = …

01:31

Show that the curve $y=\sq…

02:09

Show that the curve $y=\sq…

01:10

Show that the curve $r=2-\…

02:17

Show that the curve $ r = …

0:00

Show that the curve $r=2-\…

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

we want to show that the girl winds into X minus tangent. Inverse of X has to sign some tips being it. Why is it two X plus or minus pi half And then we want to use the's s and hopes to help us sketch the curve. Now, remember to show something has come to what we're going to want to show. Is that the limit? As X approaches plus or minus infinity of F of X minus G of X is equal to zero where this function G of X would end up being our slapped right. So let's go ahead and first get some inspiration as to which of these we should use for plus and minus infinity. So we know the limit as X approaches Infinity of XO the limit as experts, if any of ex Well, this goes to infinity, and likewise or negative. This goes to negative infinity. So that doesn't really give us anything but tangent. Inverse. So the limit as X approaches tangent inverse of x. Well, we know that this year approaches pi half and we know the limit as X approaches Negative. So negative infinity of inverse tangent would be negative pie, huh? So given this information, we might suspect that as why tends towards infinity. So our original function here it would go to X minus pi. How and then as it tends to negative infinity, it would go to X by nous negative pie half or x plus pie half. So let's go ahead and show that those two sly ass symptoms are actually the case. All right, so we want to show first the limit as ex purchase infinity of so X minus tangent and verse X. And then we're going to do minus X minus pi, huh? So here the exes will cancel out and we'll be left with the limit as X approaches Infinity of negative tangent inverse x plus pie hat because this negative here gets distributed to that. And then we already said that the limit has experts Divinity of tension Unversity pie, huh? So we get negative pie half plus high half, which is zero so that one checks out for being our slight. Ask himto as this goats towards infinity Now to show the other one works. So maybe I'll write this over here. So x minus tangent inverse of X will that tends towards X minus pi half. I know we could do the same thing for the other one. So the limit as X approaches Negative. Infinity of X minus tension in verse. Specs minus X plus. Hi. How well again. The exes here will counsel out, and then we can go ahead and let's just apply the limit right away. So the point X that we have left is right here, so that would become negative. Negative pie half. So we have negative negative pie half, and then distributing this negative to that would give us minus pi half. So these two negatives council Well, that we have pie half minus by half, which gives us zero. So that is also a slack past two. So actually I should put This is for infinity right there and then our other one. So x minus. Tanja inverse of X this year will tend towards X plus pie half when x is going too negative. Infinity. Now let's go ahead. And one other thing we might want to do if we're gonna graft this is plot our intercept. Let's do that over here in this bottom left corner. So we want to let X equal to zero. So we're gonna have why is equal to zero minus tangent. Inverse of zero. Well, Tanja inverse of zero is gonna be zeros. We get zero minus zero or just zero, so we know that the origin will be one of our points on our graph. Now, I went ahead and plotted the to slap ass in tips here, and so we know that 00 is a point. So let's go ahead and graft that really quickly. So that's going to be right here. And now we know as Ex tends towards infinity, we should tend towards X minus pi half. So the graphs should look something kind of like this getting really close to the red line. And then we also know that as extends towards negative infinity dysfunction should get really close to X plus pie half or this blue line. So this is how we could go ahead and just get a sketch of this graph without doing too much work using our to slap pass in twos

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
82
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

Caleb Elmore

Baylor University

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

01:49

Show that the curve $ y = \sqrt{x^2 + 4x} $ has two slant asymptotes: $ y = x +…

01:31

Show that the curve $y=\sqrt{x^{2}+4 x}$ has two slant asymptotes: $y=x+2$ and…

02:09

Show that the curve $y=\sqrt{4 x^{2}+9}$ has two slant asymptotes: $y=2 x$ and …

01:10

Show that the curve $r=2-\csc \theta$ (also a conchoid) has the line $y=-1$ as…

02:17

Show that the curve $ r = \sin \theta \tan \theta $ (called a $ \bf{cissoid\;o…

0:00

Show that the curve $r=2-\csc \theta$ (a conchoid) has the line $y=-1$ as a hor…
Additional Mathematics Questions

01:23

What is 20% of what number is 96?

00:13

Phong is rolling a number cube and flipping a coin .what is the probability …

02:18

Name a pair of fractions that use the least common denominator and are equiv…

00:57

Peter put $8,000 into a savings account that pays 6% interest, compounded co…

01:26

The new number, 200, is 400 less than the original number. What is the appro…

01:07

Rewrite in simplest radical form x^5/6 x^1/6 . Show each step of your proces…

01:24

PLEASE HELP ME The cost, C, to produce b baseball bats per day is modeled by…

01:27

Peter mixes 4 1/4 of orange juice, 2 1/4 cups of ginger ale, and 6 1/3 cups …

01:25

28 Rowan raised $640 in a charity walk last year. This year he raised 15% mo…

01:21

50% of the population in Alaska lives within a 50-mile radius of Anchorage. …

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