# 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

**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.

**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 .

**Q11: **

Using the squeeze theorem, calculate .

**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