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# If $4x - 9 \le f(x) \le x^2 - 4x + 7$ for $x \ge 0$, find $\displaystyle \lim_{x \to 4}f(x)$.

## $7$

Limits

Derivatives

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

this problem. Number thirty seven of the Stuart Calculus, It's edition section two point three, if for X minus sign is less than or equal to FX, which is a sin equal to X squared minus. For experts, seven. Poor X is greater than equal to zero. Find the limit his expertise for of F. So, given this information, we can attempt to find this limit. Ha ha! By use of this quiz here and possibly let's applying this limit to each of the functions this part is for for expand its time. Last ten limited his expertise for Andre unless they're equal to the limited experience for of X Squared minus for X plus seven. So here, if we apply thanks, is expertise for and we figure out the limit for the lower function on the upper function, we should be able to make ah, a announcement of what this limit should be. His expertise for for X minus nine approaches four times four or four squared minus nine and his ex approaches for for the upper function X squared minus four X plus seven Purchase four squared minus four squared for seven. Here we have sixteen minutes time which is seven. And for the upper function we also have sixteen minus sixteen plus seven, sixteen, sixteen zero. So we just have seven for that function. And because this limit has to be great for them or equal to seven and listen or equal to seven, we can definitely state that the limit X approaches for and then right the squeeze, dearie must equal seven.

#### Topics

Limits

Derivatives

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp