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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) $.

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Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 3

Calculating Limits Using the Limit Laws

Limits

Derivatives

Missouri State University

Harvey Mudd College

University of Nottingham

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.

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If $4 x-9 \leqslant f(x) \…

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Let $f(x)=x^{2}+4, x \geq …

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Let $\lim _{x \rightarrow …

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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.

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