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If $ 2x \le g(x) \le x^4 - x^2 +2 $ for all $ x $, evaluate $ \displaystyle \lim_{x \to 1}g(x) $.

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01:52

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 3

Calculating Limits Using the Limit Laws

Limits

Derivatives

Missouri State University

Baylor University

University of Michigan - Ann Arbor

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 $ 2x \le g(x) \le x^4 -…

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If $$2 x \leqslant g(x) \l…

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If 2x ≤ g(x) ≤ x4 − x2 + 2…

01:04

Given $g(x)=2 x^{2}-3 x+4 …

02:04

Let $g(x)=\left\{\begin{ar…

02:05

$\lim _{x \rightarrow-2^{2…

02:43

If $$f(x)=\left\{\begin{ar…

01:01

Decide whether the indicat…

suppose G of X is greater than or equal to two. X but less than or equal to x rays. Of the fourth power minus X squared plus two. Now, in this probably want to find the limit of the function G as X approaches one to do that, we first find me limit of the function two, X and X to the fourth power minus expert plus two as X approaches one. And so we have limits as X approaches one of two. X. This is equal to two times one, which is to and the limit as X approaches one of x rays to the fourth power minus X squared plus two. This is equal to one. Race to the fourth power minus one squared plus two. Or that's just too, which tells us that the limit as X approaches one of two X. This is equal to the limit as X approaches one of x rays to the fourth power minus X ray plus two. And this is equal to one. Know that in squeeze theorem, if we have F of X less than or equal to G of X less than or equal to H of X. And we found that the limit as X approaches A of F of X equals the limit as X approaches A of H of X, then the limit of G as X approaches mm will be equal to the limit of the two functions. Let's say this is equal to L. So this will also be equal to L. Therefore, by squeeze theorem, do you limit all the function G of X as X approaches one is equal to one?

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