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

Let $ f(x) = 1/x $ and $ g(x) = 1/x^2 $. (a) F…

02:36

Question

Answered step-by-step

Problem 47 Medium Difficulty

Suppose $ f $ and $ g $ are continuous functions such that $ g(2) = 6 $ and $ \displaystyle \lim_{x \to 2} [3f(x) + f(x)g(x)] = 36 $. Find $ f(2) $.


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Ma. Theresa Alin
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Ma. Theresa Alin

Numerade Educator

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

More Answers

02:58

Daniel Jaimes

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 5

Continuity

Related Topics

Limits

Derivatives

Discussion

You must be signed in to discuss.
ZR

Zachariah R.

February 2, 2022

how did you get 9?

MA

Maitha A.

September 12, 2021

MA

Maitha A.

September 12, 2021

how did you get the 9 ?

Top Calculus 1 / AB Educators
Grace He
Heather Zimmers

Oregon State University

Kayleah Tsai

Harvey Mudd College

Caleb Elmore

Baylor 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

0:00

Suppose $ f $ and $ g $ ar…

04:42

Suppose $f$ and $g$ are co…

02:34

Suppose f and g are contin…

03:35

Suppose f and g are contin…

02:21

Use the definition of cont…

01:03

Given $f(x)=\frac{2 x}{x^{…

02:09

Use the definition of cont…

02:08

Determine whether $f$ is c…

01:14

Determine whether $f$ is c…

03:22

Use the definition of cont…

01:26

The limit represents $f^{\…

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

Video Transcript

suppose F and G are continuous functions such that G F two is equal to six. And the limit of three times F of X plus F of X times G of X as X approaches to is 36. And here we want to find ff two. And by definition of continuity, if F and G are continuous functions, then we have the limit as X approaches to of F of X, this is equal to F F two. And the limit as X approaches to of G of X, this is equal to G F two. Now, since june of two is equal to six, then this is equal to six. And so the limit as X approaches to of three times F of X plus F of X times G fx This is equal to the limit as X approaches to of three times F of X plus, we have the limit as X approaches to of f of x times geo vex, which we can be right into three times the limit as X approaches to of F of X plus, Yes, the limit as X approaches to of F of X. This times the limit as X approaches to of G of X. Now, if we factor out the limit of F of X as X approaches to, we have limit as X approaches to of F of X this times three plus, the limit as X approaches to G fx given that this equals 36 the limits of G of X as X approaches to six, then we have 36. This is equal to the limit as X approaches to of F of X, this times three plus six. And since this is nine, we have the limit as X approaches to of F of X. This is equal to 36/9 or four. And because F of X container was then this limit of F of X as X approaches to this is equal to the value of F at two. Therefore, F of to this is equal to 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
162
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
70
Hosted by: Alonso M
See More

Related Topics

Limits

Derivatives

Top Calculus 1 / AB Educators
Grace He

Numerade Educator

Heather Zimmers

Oregon State University

Kayleah Tsai

Harvey Mudd College

Caleb Elmore

Baylor 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

0:00

Suppose $ f $ and $ g $ are continuous functions such that $ g(2) = 6 $ and $ \…

04:42

Suppose $f$ and $g$ are continuous functions such that $g(2)=6$ and $\lim _{x …

02:34

Suppose f and g are continuous functions such that g(6) = 3 and lim_ [3f(x) f(x…

03:35

Suppose f and g are continuous functions such that g(6) = 6 and lim x → 6 [3f(x…

02:21

Use the definition of continuity to determine whether $f$ is continuous at a. $…

01:03

Given $f(x)=\frac{2 x}{x^{3}+216},$ find $$\lim _{x \rightarrow-6} f(x)$$

02:09

Use the definition of continuity and the properties of limits to show that the …

02:08

Determine whether $f$ is continuous at $c .$ $$ f(x)=x^{3}-3 x^{2}+2 x-6 \quad …

01:14

Determine whether $f$ is continuous at $c .$ $$ f(x)=\frac{x^{2}-6 x}{x^{2}+6 x…

03:22

Use the definition of continuity and the properties of limits to show that the …

01:26

The limit represents $f^{\prime}(c)$ for a function $f$ and a number $c .$ Find…
Additional Mathematics Questions

01:42

Question 3
Find the domain and range of the function graphed below:
Do…

01:28

Use transformations of the graph of f(x) =X? to determine the graph of the g…

03:38

Use the graph to evaluate the expressions in (a) - (f)
(a) Evalu…

05:19

For Questions 16 and 17, use the figure at the right: Round to the nearest t…

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