suppose-f-and-g-are-continuous-functions-such-that-g26-and-lim-_x-rightarrow-23-fxfx-gx36-find-f2-2

Question

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

Agata Pavone · Accepted Answer

what let&#x27;s supposed to have two functions f n g off continues above continuous. And we also know that that&#x27;s why did Containers We also know that G job two is equal six and we know also that limit when X approaches to free Al Flex Plus in flex geo eggs equal 36 We want to know divine you effort to question Mark So what can we do? What we know that the two functions are continuous So we know that the limit when X purchase to the limit of our fullbacks is equal As to onda limit while X approaches to a t you fax is equal to yours too. This is because the two functions are continues. Dad, we know Geo, Do we want to know why? Foot, Let&#x27;s look at this limit whose value is known? Fact e six. So we have the limit off the sun off two functions. The 1st 1 is free of X and the 2nd 1 is the product off f of X to your backs. So we can say that the name is when except purchase to off free your backs plus have for Max to your ex equal This is, the sum often functions. The limit off the sun is equal to the sum off the limits On the product of a Kirsten, The limit off Causton times a function is equal by thinking about the properties of millions is equal to the constant times limit are the function and then the limit of Osama see equal to the son of the limits. And we also know that the Lear it on the product of two function is equal to the product off the to limits. Name it off the first function times. Name it when X approaches the same money to off the second function. So let&#x27;s see now. Now we know that the two functions f engineer continuous attack sequence to So we know that live it when x a purchase to over four backs. We know that is equal toe to Plus we know that limit off. Expect for when X separatists to of a fire effort taxes equal effort to guys and see you too. That&#x27;s because they&#x27;re two functions are continues and we also know that this name it the new German is equal to 56. So we can Blufgan divine you off you too. And so we have free after two laugh. What you have to is 662 Ikhwan fantasist eggs. It means free plus six is 9/2 of to equal. 36. It means effort to is equal for Oh, this is then the question is just what we were asked at the beginning. Find the value off I talked to.

Ma. Theresa Alin · Answer

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.

Alan Ghazarians · Answer

is that we have this limit. What can we say about the value of F of three com one we don&#x27;t know, right? There could be, Ah, hole Or maybe and ask himto so we don&#x27;t know. But if F is continuous, then f a three common one is equal to six.

Elizabeth Xu · Answer

So here we&#x27;re looking to find the limit as X approaches negative six of f of X. We can stop a plugging in different numbers into our table values journey with numbers from the left hand side such as negative 6.1 negative 6.1 and negative 6.1 That means that our Kovacs is equal to 1.11 Could we get 11.11 in 1 11? Wait 11 So, as you can see from the left inside, our limit is going towards infinity. On the right hand side, we can plug in numbers such as negative 5.9 negative 5.99 negative 5.999 which gets us affects. We have 1.11 negative. 11.11 United have won 11.11 So here our limit is getting towards negative infinity. So that means because I left him. Limit does not equal the right hand limit. That means our limit when, except which is negative. Six of f of X does not exist

Khoi V · Answer

and oh, this is proper. 13 Give you that to function F and G being continuous. And Val Ooh, that you have for if a tree is five and its limit things three. All right, so let&#x27;s get started. First of all, we need to see what they got. You limit X go to three to F x minus Z f x. So, according to some rule about limit, because he&#x27;s a boat continuous, so we could use some rule here. We can actually do the limit to the limit effort. Backs were executed tree and then minus limits. Max, go to tree G of X. This we&#x27;re using rule number two and number three and in continually function in the limits rule. All right now the number two which is state there. But because the function F is continuous, it&#x27;s a limited after court victory will be Africa tree all right and same thing That&#x27;s limit will be G up tree because F and G continuous. So the limits f X go to three will be f victory and the limits Exco tree of G of x will be easy up tree and we we was given that this whole thing was four to begin with. Right? Using that for right here. So now what? Do we have this reread it. We got four equal to to Africa tree. They&#x27;re African tree was given two ss fi have a tree equal to fi and minus g up tree So now you confined you grease or four ico 10 minor gee up tree So you&#x27;re g up tree Must be so six That&#x27;s it. See you in the next video.

Julian Gerber · Answer

So we have the function f of X, and we want to determine whether F of X is continuous at X equals 36. So, first of all, let&#x27;s find out what f of 36 is. Make sure it&#x27;s defined. So f of 36 equals 36 times. Route 36 over 36 minus six squared. We simplify that. Route 36 is just six. So you have 30 to 6 times six, which is, um, 2 16 over 36 months. Six is 30 30 squared is 900. So we have to 16 over 900 which can be simplified, but it doesn&#x27;t matter. Next, we have to find out that the limit exists. So the limit as X approaches 36 of F of X. And we don&#x27;t have to worry about left hand and right hand limits because as the um, the function is the same. It&#x27;s the same function, um, both to the left of 36 to the right of 36. So it&#x27;s gonna be approaching the same limit value. And when we substitute in 36 for acts are answer isn&#x27;t indeterminant. It&#x27;s not 0/0 or infinity over infinity. It&#x27;s a constant values are. Limit is just that same constant value. So we&#x27;ve determined that the limit exists and that it&#x27;s equal to the function. Value F of 36 therefore F of X is continuous at X equals 36.

Problem

$12-13=$ Use the definition of continuity and the…

Problem 11 Easy Difficulty

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

Answer

$$
4=f(2)
$$

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James Stewart

Essential Calculus Early Transcendentals

Heather Z.

Caleb E.

Michael J.

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Precalculus Review - Intro

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$$4=f(2)$$

Essential Calculus Early Transcendentals

Heather Z.

Caleb E.

Michael J.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

James StewartEssential Calculus Early Transcendentals

Heather Z.

Caleb E.

Michael J.

Joseph L.

$$
4=f(2)
$$

James Stewart

Essential Calculus Early Transcendentals