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

The figure shows a fixed circle $ C_1 $ with equa…

05:35

Question

Answered step-by-step

Problem 65 Hard Difficulty

Is there a number $ a $ such that
$$ \lim_{x \to -2}\frac{3x^2 + ax + a + 3}{x^2 + x - 2} $$
exists? If so, find the value of $ a $ and the value of the limit.


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 3

Calculating Limits Using the Limit Laws

Related Topics

Limits

Derivatives

Discussion

You must be signed in to discuss.
Top Calculus 1 / AB Educators
Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

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

07:08

Is there a number $a$ such…

05:21

Is there a number a such t…

00:44

Find the limit, if it exis…

00:46

Find the limit, if it exis…

04:41

Find the limit, if it exis…

02:30

Determine the infinite lim…

01:44

Determine the infinite lim…

01:39

Find the limit.
$$
\…

00:38

Find the limit.
$\lim …

00:16

Find the limit.
$$
\…

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

Video Transcript

this problem Number sixty five of this store Calculus aesthetician section two point three Their number. Hey, such that eliminates X approaches. Negative, too. Of the function three X squared plus a experts able astri, divided by the quantity X squared plus X minus two exists. If so, find the value of a and the value filament. The reason there's concern whether this limit exists or not, is two to the denominator. Let's see what happened there only plaguing negative too. And two squared minus two minus two equals four minus two minutes to its hero. So then I made her a zero. And we have a concerned whether this exists or not run The only way that we're going to get ah, this limit equals zero or to exist is that even even though the denominator is zero, we'LL have an opportunity to have this limit exist. If the numerator is also zero. So when would that occur? I think this Oh no. And let's solve at negative too. And that sulfur value, eh, that makes this a function include a zero. Okay, so we have three times of forest talk, thanks to a plus. A plus three equals zero things to say is equal to NATO and moving that to the right side kiss positivity and we see that he is equal to fifteen. This is the number that we need in order for this limit to exist. So this is a part one year from the value of a a mystical fifteen because that makes the neuron are equal zero. Now, how do we find the value the limit? Well, we take the new polynomial three minutes care it is three X squared A is fifteen points or fifteen x, and again in his fifteen plus three is eighteen. I want a better by this opponent Meal X squared plus X minus two. We'LL be able to evaluate estimate by simplifying these polynomial. For example, the denominator reduces to expose, to add factors to expose, to multiply it by express one and the new marina I should tractor as such Explosives too. Three AKs Pleasant night, right? Because we get three x squared plus x X plus name That's fifteen nine times two is eighteen. At this point, we can see that in next was two councils and this was intended because this term is the part that made the denominator zero. And we chose the appropriate value of eight to make ah, to have their be affect. Er for the numerator. Cancel out when exes equal to negative too, to know we're left with three X plus nine. Tired of my experience. One and the value in and negative too. Getting into six plus thing, all running at three. And this casus value, I think it a one over our limit.

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
64
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
42
Hosted by: Alonso M
See More

Related Topics

Limits

Derivatives

Top Calculus 1 / AB Educators
Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

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

07:08

Is there a number $a$ such that $$\quad \lim _{x \rightarrow-2} \frac{3 x^{2}+…

05:21

Is there a number a such that the following limit exists? (If an answer does no…

00:44

Find the limit, if it exists. $$ \lim _{x \rightarrow-x} \frac{2-x^{2}}{x+3} $$

00:46

Find the limit, if it exists. $$ \lim _{x \rightarrow x} \frac{-x^{3}+2 x}{2 x^…

04:41

Find the limit, if it exists. $$ \lim _{x \rightarrow-3^{-}}\left(\frac{x}{x^{2…

02:30

Determine the infinite limit. $\lim _{x \rightarrow-3^{-}} \frac{x+2}{x+3}$

01:44

Determine the infinite limit. $\lim _{x \rightarrow-3^{+}} \frac{x+2}{x+3}$

01:39

Find the limit. $$ \lim _{x \rightarrow \infty} \frac{x^{3}-2 x^{2}+3 x+1}{x^{2…

00:38

Find the limit. $\lim _{x \rightarrow 2^{+}} \frac{x-3}{x-2}$

00:16

Find the limit. $$ \lim _{x \rightarrow 3}\left(x^{2}+2\right) $$
Additional Mathematics Questions

00:47

"answer the question 8 with complete explanation class 7
00.
8 o[…

02:17

'Pls tell answer fast fast
In a class test containing 15 questions, …

02:07

"Answer this please, thank you
Consider the following sets: The univ…

03:18

'please tell me the answer
12. Sachin bought 4 packs of white T-shir…

02:37

'FIND THE H.C.F OF THE FOLLOWING
(e) 690, 966 and 1150 () 738, 1…

03:46

'please answer this question
Project 4 Mathematical Crosswords puzzl…

02:26

"URGENT HELP 20 POINTS HELP HELP PLEASE
The linear model represents …

02:16

'Which congruency statement is true?
1) ⦟ACX ≅ ⦟BXD
2) ACX ≅ ⦟DXB…

02:53

'What is the solution of the given matrix equation?F3 1-115 23 1
Pao…

02:29

'Due to heavy storm an electric wire got bent as shown in figure. It fo…

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
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started