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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 $f(2)$

$$4=f(2)$$

Calculus 1 / AB

Chapter 1

FUNCTIONS AND LIMITS

Section 5

Continuity

Functions

Limits

Continuous Functions

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Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

0:00

Suppose $ f $ and $ g $ ar…

00:40

Suppose that $ \lim_{(x, y…

01:03

Given $f(x)=\frac{2 x}{x^{…

02:21

If $f$ and $g$ are continu…

02:09

Use the definition of cont…

01:24

If $ f' $ is continuo…

00:30

Evaluate $f(3)$ if $\lim _…

03:22

02:42

Suppose that $\lim _{(x, y…

07:14

If $f^{\prime}$ is continu…

what let's supposed to have two functions f n g off continues above continuous. And we also know that that'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'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'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's because they'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.

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