Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

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

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Ma. Theresa Alin

Numerade Educator

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

02:58

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 5

Continuity

Limits

Derivatives

Zachariah R.

February 2, 2022

how did you get 9?

Maitha A.

September 12, 2021

how did you get the 9 ?

Oregon State University

Harvey Mudd College

Baylor University

Lectures

04:40

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.

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.

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

02:21

Use the definition of cont…

01:03

Given $f(x)=\frac{2 x}{x^{…

02:09

02:08

Determine whether $f$ is c…

01:14

03:22

01:26

The limit represents $f^{\…

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.

View More Answers From This Book

Find Another Textbook

01:42

Question 3Find 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…