# Worksheet: The Squeeze Theorem

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

Q1:

Consider the following arc of a unit circle, where ray is inclined at radians. What, in terms of , are the coordinates of ?

• A
• B
• C
• D

Write the following inequalities in terms of , , and :

• A
• B
• C
• D

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

• A does not exist.
• B
• C

Q2:

Given that the function is continuous, which of the following can we conclude from the squeeze theorem? • A
• B
• C
• D
• EThe limit of as does not exist.

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 ?

• A
• B
• C
• D
• E

Q4:

In deciding that , which assumptions do we use? Select all valid answers.

• A
• B and
• C does not exist.
• D and
• E

Q5:

Calculate using the squeeze theorem.

Q6:

The figure shows the graphs of functions and with for between 2 and 3.8. What does the squeeze theorem tell us about a continuous function whose graph lies in the shaded region over the interval ?

• A
• B
• C
• D
• EThe limit does not exist.

Q7:

Knowing that the squeeze theorem applies when the limit is taken at , determine .

Q8:

Using the squeeze theorem, check whether the following statement is true or false:

If , then .

• ATrue
• BFalse

Q9:

Use the squeeze theorem to evaluate .

Q10:

Use the squeeze theorem to evaluate .

Q11:

Using the squeeze theorem, calculate .

Q12:

Given that , find .

• AThe limit does not exist.
• B1
• C4
• D
• E

Q13:

Calculate using the squeeze theorem.

Q14:

Evaluate the limit .

Q15:

Given the function , such that for all , find .

• A
• B
• CThe limit does not exist.
• D0
• E