# Worksheet: Limits and Limit Notation

In this worksheet, we will practice using limit notation and exploring the concept of a limit.

**Q1: **

What is the correct notation that describes the following statement?

As approaches 0 , approaches .

- A
- B
- C
- D

**Q2: **

What does the notation mean?

- A is undefined at and at .
- BAs gets closer and closer to 2 , gets closer and closer to 5 .
- CThe value of at is equal to the value of at .
- DAs gets closer and closer to 5 , gets closer and closer to 2 .
- EThe value of the function is 2 at .

**Q3: **

The following table gives the values of the function at several values of .

2.99 | 2.999 | 2.9999 | 2.9999 | 3.00001 | 3.0001 | 3.001 | 3.01 | |

What does the table suggest about the value of ?

- AThe value of the limit equals 2.
- BThe value of the limit equals 3.
- CThe value of the limit equals .
- DThe value of the limit equals .

**Q4: **

The following table gives the values of the function at several values of .

What does the table suggest about the value of ?

- AThe value of the limit equals .
- BThe value of the limit equals .
- CThe value of the limit equals .
- DThe value of the limit equals .
- EThe value of the limit does not exist.

**Q5: **

True or False: If , then it is possible that the function could be undefined at .

- AFalse
- BTrue

**Q6: **

True or False: If , then must be equal to .

- ATrue
- BFalse

**Q7: **

The following figure represents the graph of the function .

What does the graph suggest about the value of ?

- A
- B does not exist.
- C
- D
- E

**Q8: **

The following figure represents the graph of the function .

What does the graph suggest about the value of ?

- AThe value of the limit equals .
- BThe value of the limit equals 3.
- CThe limit does not exist.
- DThe value of the limit equals .
- EThe value of the limit equals 2.

**Q9: **

The following figure is the graph of the function , where .

What is the value of ?

- A
- B
- C
- D
- E is undefined.

What does the graph suggest about the value of ?

- A
- B
- C
- D does not exist.
- E

**Q10: **

The following figure is the graph of the function , where .

What is the value of ?

- A
- B is undefined.
- C
- D
- E

What does the graph suggest about the value of ?

- A
- B
- C
- D does not exist.
- E

**Q11: **

Which of the following statements is **not** the same as saying that ?

- AAs gets closer and closer to 8 , gets closer and closer to 3 .
- BWe can make as close as we like from 3 by taking sufficiently close to 8 .
- C approaches 3 as approaches 8 .
- D is equal to .