Lesson: The Squeeze Theorem Mathematics • Higher Education

In this lesson, we will learn how to use the squeeze (sandwich) theorem to evaluate some limits when the value of a function is bounded by the values of two other functions.

Lesson Plan

Students will be able to

understand the squeeze theorem,
apply the squeeze theorem to functions combining polynomials, trigonometric functions, and quotients.

Lesson Video

Lesson Worksheet

Q1:

Consider the following arc of a unit circle, where ray is inclined at radians.

What, in terms of , are the coordinates of ?

Write the following inequalities in terms of , , and :

By dividing your inequalities by , using the squeeze theorem and the fact that , which of the following conclusions can you draw?

Q2:

Given that the function is continuous, which of the following can we conclude from the squeeze theorem?

Q3:

The graph shown is that of the function .

Given that is a function such that for all , which of the following functions can be such that , so that we can show that ?