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

Prove the statement using the $ \varepsilon $, $ …

01:50

Question

Answered step-by-step

Problem 22 Medium Difficulty

Prove the statement using the $ \varepsilon $, $ \delta $ definition of a limit.

$ \displaystyle \lim_{x \to -1.5}\frac{9 - 4x^2}{3 + 2x} = 6 $


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 4

The Precise Definition of a Limit

Related Topics

Limits

Derivatives

Discussion

You must be signed in to discuss.
Top Calculus 1 / AB Educators
Grace He
Anna Marie Vagnozzi

Campbell University

Michael Jacobsen

Idaho State University

Joseph Lentino

Boston College

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

03:44

Prove the statement using …

02:06

Prove the statement using …

04:44

$19-32$ Prove the statemen…

03:21

Prove the statement using …

04:47

Prove the statement using …

0:00

Prove the statement using …

01:54

Prove the statement using …

07:16

Prove the statement using …

02:28

Prove the statement using …

0:00

Prove the statement using …

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

Video Transcript

prove this statement. This is problem number twenty two of these to a cactus. In addition, Section two point four through the statement using the Absalon Delta definition of the limit, the limit is experts is negative one point five of the quantity and I'm minus four x squared, divided by the quantity three plus two X is equal to six. And here to the right, we have a summary of our absolute out. The definition of a limit is limited. It perches as a CZ expert initiative. One point five of this function is equal to six as long as there is an absolute great in zero for every Absalon great. And so that there is adulterated Terrel such that if the absolutely the difference between X and A in this case make it a one point five is lesson doctor, then they absolutely the function and the limit. That difference of the absolutely of that difference is less than Absalom. So we begin with our second equality and right the function nine minus for X squared. That quantity, divided by the quantity three plus two eggs minus the limit the limit is equal to six is less than absolute Absalon. We want to simplify distraction. Possibly if that helps simplify out of this further. We noticed that this is a difference of squares. This is three squared. This is to X squared. So we split it up as three plus two x and three minus two X denominator remains three plus two x six. Here we noticed that in the denominator, ACS is not allowed earthy value of negative one point five is not a little mean. And we you choose to assume that X only a purchasing at one point five and does not equal one point five. And since this is true, then these two Kim council thes two terms leaving us with three minutes to X minus six. If we're right that combining three and then ninety six, we get negative two X minus three Less than absolute Here we confected out. See, we can factor out or divided, divided by negative too, Charlie. And pull that out. So native to give us this X plus three or two listing Absalon notice that this is appropriate because they have to multiply by X Gives this thing up to x ray. Want to play by three over two times this number three This absolutely of the negative, too, is the same man's the absolutely positive, too. And that, too, can be divided on both sides and our final statement as X plus three. House is less than absolute over too. And we make the observation that air first and equality is X minus a, which is Ah, negative one point five. So, plus one point five must be lesson. Delta one point five is another form of the fraction three halves. And we make observation that this inequality and the one we found her previously are almost equivalent on their equivalent for Delta. He cools to Absalon over too. And here is our relationship between Delta Epsilon. Essentially, we have proven that there exists a delta greater than zero for every apps on agree with Theo. And that was thie proof for this limit. Through this absolute off the definition of limited that as long as Delta is equal to Absalon or two a cz an example, then this statement is proved

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
94
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
54
Hosted by: Alonso M
See More

Related Topics

Limits

Derivatives

Top Calculus 1 / AB Educators
Grace He

Numerade Educator

Anna Marie Vagnozzi

Campbell University

Michael Jacobsen

Idaho State University

Joseph Lentino

Boston College

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

03:44

Prove the statement using the $\varepsilon, \varepsilon$ definition of a limit.…

02:06

Prove the statement using the $\varepsilon, \varepsilon$ definition of limit. …

04:44

$19-32$ Prove the statement using the $\varepsilon, \delta$ definition of a lim…

03:21

Prove the statement using the $ \varepsilon $, $ \delta $ definition of a limit…

04:47

Prove the statement using the $ \varepsilon $, $ \delta $ definition of a limit…

0:00

Prove the statement using the $ \varepsilon $, $ \delta $ definition of a limit…

01:54

Prove the statement using the $\varepsilon, \delta$ definition of a limit. $$\…

07:16

Prove the statement using the $ \varepsilon $, $ \delta $ definition of a limit…

02:28

Prove the statement using the $\varepsilon, \delta$ definition of limit. $\l…

0:00

Prove the statement using the $ \varepsilon $, $ \delta $ definition of a limit…
Additional Mathematics Questions

01:17

The rabbit population in a certain area is 500% of last year's populati…

01:07

Use benchmarks to estimate the sum 11/15 + 1/8

01:38

1. A tank contains 2,450 gallons of fuel. The changes in the number of
ga…

00:30

Given the set : {5, 8, 8, 10, 10, 11, 15, 17, 20), what is the probability o…

01:31

Liam has a bag of b beads. He gives 20 beads to his sister. He then uses all…

00:32

A machine cuts 25 circuit boards every 5 minutes. What is the unit rate of p…

00:45

Straws are sold in packs and boxes.
there 15 straws in each pack.
ther…

02:48

Which expression would be easier to simplify if you used the associative pro…

01:46

The standard diameter of a golf ball is 42.67 mm. A golf ball factory does q…

01:21

what is 56+32 distributive property to factor out the greatest common factor…

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