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

For the limit $$ \lim_{x \to -\infty} \frac{1 - 3…

03:43

Question

Answered step-by-step

Problem 72 Hard Difficulty

For the limit $$ \lim_{x \to \infty} \frac{1 - 3x}{\sqrt{x^2 + 1}} = -3 $$ illustrate Definition 7 by finding values of $ N $ that correspond to $ \varepsilon = 0.1 $ and $ \varepsilon = 0.05 $.


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Daniel Jaimes
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Daniel Jaimes

Numerade Educator

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

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Related Topics

Limits

Derivatives

Discussion

You must be signed in to discuss.
Top Calculus 1 / AB Educators
Grace He
Catherine Ross

Missouri State University

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Limits - Intro

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Join Course
Recommended Videos

01:11

$$ \begin{array}{l}{\text …

03:08

For the limit
$$\lim _{…

03:43

For the limit $$ \lim_{x \…

05:56

For the limit
$$\lim _{…

04:51

Given that $ \displaystyle…

01:25

Compute the indicated limi…

00:40

Determine each limit.
$…

05:49

For the limit
$$\lim _{…

Watch More Solved Questions in Chapter 2

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 14
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
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81

Video Transcript

This is problem number seventy two of the sewer calculus eighth edition, section two point six for the limit. The limit is ex purchase infinity one minus three X divided by square root of the quantity X squared plus one equals three. Kill a street definition seven By finding values bin they correspond to absolutely cools to Sierra point one and absolutely equals to zero point zero fighters. And our definition, it has to do with defining there that the difference between the function and its limit the distance between the two or the absolute value be less than the value Absalon provided that you have an ex and greater than a certain value and right to the school together. And in our case, this is our function If and this is our limit own All right. So we need to find about you end that essentially guarantees of the function is less than Absalon away from the limit. So take a look at this function and we plant this function here one minus three x divided by the square root of the quantity X squared plus one. Ah, and we see that dysfunction approaches approaches Negative three. But we know that as the limit is, X approaches. Infinity Little, many calls native. Three. That means it'LL person ing into three but never be equal to negative three. So, really, when we're solving this problem here that we want the function to be within point one of its limit. Ah, that's exactly what determines our in. So within point one of negative three Centenary goes beyond negative three or equals negative three within point one means negative two point nine of negative three Thank you two point. And is Sarah quaint one away from negative three. So you need a next value at least equal to eleven point three to be able to achieve a value on the function within a zero point one of the limit, which is equal to make it three. So for this first step, Swan Lun is eleven point three Now. As we hit more precise with our Absalon point o five, we expect the larger Valley event how much more strict, stricter value. And that's exactly what we've seen. The function. It's causing negative three as we continued to the extraction and we need an X X value at least equal to twenty one point four In order to be within a point, there are five over the limit. So for this Absalon, our numbers approximately twenty one point four.

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
83
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
53
Hosted by: Alonso M
See More

Related Topics

Limits

Derivatives

Top Calculus 1 / AB Educators
Grace He

Numerade Educator

Catherine Ross

Missouri State University

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Limits - Intro

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Join Course
Recommended Videos

01:11

$$ \begin{array}{l}{\text { For the limit }} \\ {\quad \lim _{x \rightarrow \in…

03:08

For the limit $$\lim _{x \rightarrow \infty} \frac{3 x}{\sqrt{x-3}}=\infty$$ …

03:43

For the limit $$ \lim_{x \to -\infty} \frac{1 - 3x}{\sqrt{x^2 + 1}} = 3 $$ illu…

05:56

For the limit $$\lim _{x \rightarrow-\infty} \frac{1-3 x}{\sqrt{x^{2}+1}}=3$$ …

04:51

Given that $ \displaystyle \lim_{x \to 2}(5x - 7) = 3 $, illustrate Definition …

01:25

Compute the indicated limit. $$\lim _{x \rightarrow \infty} \frac{2 x^{3}-7}{x+…

00:40

Determine each limit. $$\lim _{x \rightarrow \infty} \frac{1-7 x^{3}}{x^{2}+7 x…

05:49

For the limit $$\lim _{x \rightarrow 1}\left(4+x-3 x^{3}\right)=2$$ illustrat…

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