/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 97 Squeeze Theorem In your own word... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 97

Squeeze Theorem In your own words, explain the Squeeze Theorem.

Short Answer

Expert verified
The Squeeze Theorem in calculus states that if a function is 'squeezed' between two other functions that converge to the same limit at a certain point, then the squeezed function must also converge to the same limit. Think of it as a car trapped between two other cars on a highway. If the front and back cars slow down simultaneously, the middle car also has to slow down to avoid collision.

Step by step solution

01

Understanding the Squeeze theorem

The Squeeze Theorem is a concept in calculus which states that if function f is 'squeezed' between two other functions g and h at a certain point, and if g and h converge to the same limit at that point, then the squeezed function f must also converge to the same limit.
02

Breaking Down the Theorem

On the number line, if you have three points a, b, and c such that a <= b <= c, then you can say that b is squeezed between a and c. In the Squeeze Theorem, instead of points on a line, we have functions on a graph. If function f(x) is always between functions g(x) and h(x) and if g(x) and h(x) converge to the same limit when x approaches a certain value, then f(x) must also converge to the same limit.
03

Relating Squeeze Theorem to Real Life

A real-life scenario for the Squeeze Theorem could be a car trapped in between two other cars on a highway all moving at the same speed. If the cars in front and back decide to simultaneously slow down, assuming the car in the middle doesn't want to collide, it has to also slow down to the same speed.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Testing for Continuity In Exercises \(77-84\) , describe the interval(s) on which the function is continuous. $$ f(x)=\frac{x}{x^{2}+x+2} $$

Continuity of a Function In Exercises \(27-30,\) discuss the continuity of each function. $$ f(x)=\frac{1}{2}[ | x] ]+x $$

Removable and Nonremovable Discontinuities In Exercises \(35-60,\) find the \(x\) -values (if any) at which \(f\) is not continuous. Which of the discontinuities are removable? \ $$ f(x)=\left\\{\begin{array}{ll}{x,} & {x \leq 1} \\ {x^{2},} & {x>1}\end{array}\right. $$

Finding a Limit In Exercises \(7-26\) , find the limit (if it exists). If it does not exist, explain why. $$ \lim _{x \rightarrow 1} f(x), \text { where } f(x)=\left\\{\begin{array}{ll}{x^{3}+1,} & {x<1} \\ {x+1,} & {x \geq 1}\end{array}\right. $$

True or False? In Exercises \(103-106,\) determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If \(\lim _{x \rightarrow c} f(x)=L\) and \(f(c)=L,\) then \(f\) is continuous at \(c\)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.