How to Do Squeeze Theorem. Though Squeeze Theorem can theoretically be used on any set of functions that satisfy the above conditions, it is particularly useful when dealing with sinusoidal functions. As with most things in mathematics, the best way to illustrate how to do Squeeze Theorem is to do some Squeeze Theorem problems.
LIMITS OF FUNCTIONS USING THE SQUEEZE PRINCIPLE
The following problems involve the algebraic computation of limits using the Squeeze Principle,which is given below.The Squeeze Theorem. If there exists a positive number p with the property that. For all x that satisfy the inequalities then Proof (nonrigorous). This statement is sometimes called the ``squeeze theorem' because it says that a function ``squeezed' between two functions approaching the same limit L must also approach L. Calculus I - Limits - The Squeeze Theorem - A More Complicated Example. The Infinite Looper. Calculus I - Limits - The Squeeze Theorem - 2 Examples.
SQUEEZE PRINCIPLE : Assume that functions f , g , and h satisfy
and
.
Then
Squeeze Theorem Ap Calculus
.
(NOTE : The quantity A may be a finite number, , or . The quantitiy L may be a finite number, , or .)
The Squeeze Principle is used on limit problems where the usual algebraic methods (factoring, conjugation, algebraic manipulation, etc.) are not effective. However, it requires that you be able to ``squeeze' your problem in betweentwo other ``simpler' functions whose limits are easily computable and equal. The use of the Squeeze Principle requires accurate analysis, deft algebra skills, and careful use of inequalities.
- PROBLEM 1 : Compute .
Click HERE to see a detailed solution to problem 1.
- PROBLEM 2 : Compute .
Click HERE to see a detailed solution to problem 2.
- PROBLEM 3 : Compute .
Click HERE to see a detailed solution to problem 3.
- PROBLEM 4 : Compute .
Click HERE to see a detailed solution to problem 4.
- PROBLEM 5 : Compute .
Click HERE to see a detailed solution to problem 5.
- PROBLEM 6 : Compute .
Click HERE to see a detailed solution to problem 6.
- PROBLEM 7 : Compute .
Click HERE to see a detailed solution to problem 7.
- PROBLEM 8 : Assume that exists and . Find .
Click HERE to see a detailed solution to problem 8.
- PROBLEM 9 : Consider a circle of radius 1 centered at the origin and an angle of radians, , in the given diagram.
a.) By considering the areas of right triangle OAD, sector OAC, and right triangle OBC, conclude that
.
b.) Use part a.) and the Squeeze Principle to show that
Click HERE to see a detailed solution to problem 9.
- PROBLEM 10 : Assume that
Show that f is continuous at x=0 .
Click HERE to see a detailed solution to problem 10.
Click HERE to return to the original list of various types of calculus problems.
Your comments and suggestions are welcome. Please e-mail any correspondence to Duane Kouba by clicking on the following address :
Squeeze Theoremap Calculus Calculator
Duane KoubaWed Oct 15 16:55:51 PDT 1997