# Worksheet: Limits and Limit Notation

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

**Q2: **

What does the notation mean?

- AAs gets closer and closer to 5 , gets closer and closer to 2 .
- BAs gets closer and closer to 2 , gets closer and closer to 5 .
- CThe value of at is equal to the value of at .
- DThe value of the function is 2 at .
- E is undefined at and 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 .
- BThe value of the limit equals .
- CThe value of the limit equals 2.
- DThe value of the limit equals 3.

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

**Q8: **

The following figure represents the graph of the function .

What does the graph suggest about the value of ?

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

**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
- E does not exist.

**Q11: **

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

- A is equal to .
- B approaches 3 as approaches 8 .
- CWe can make as close as we like from 3 by taking sufficiently close to 8 .
- DAs gets closer and closer to 8 , gets closer and closer to 3 .

**Q12: **

If , what can we say about ?

- A
- B
- C
- DWe cannot draw any conclusions about .
- E

**Q13: **

Given that , what is the value of ?

- A10
- B20
- C7
- D5
- E13

**Q14: **

Given that , which of the following statements must be false?

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

**Q15: **

Given that , which of the following statements must be true?

- A
- B
- C
- D
- ENone of the above