In this worksheet, we will practice determining whether the limit of a function at a certain value exists.

**Q2: **

Discuss the existence of given

- AThe limit exists and equals .
- BThe limit exists and equals 20.
- CThe limit does not exist because does not exist.
- DThe limit does not exist because .

**Q3: **

Discuss the existence of given

- AThe limit exists and equals .
- BThe limit exists and equals 5.
- CThe limit does not exist because does not exist.
- DThe limit does not exist because .
- EThe limit does not exist because does not exist.

**Q4: **

Discuss the existence of given

- AThe limit exists and equals 0.
- BThe limit does not exist because .
- CThe limit exists and equals .
- DThe limit exists and equals 1.
- EThe limit exists and equals .

**Q5: **

Discuss the existence of given

- AThe limit exists and equals 0.
- BThe limit does not exist because .
- CThe limit exists and equals 3.
- DThe limit exists and equals 5.
- EThe limit exists and equals 7.

**Q6: **

Determine if it exists, where

- A
- B1
- C4
- D5

**Q7: **

Discuss the existence of the limit as given

- AThe limit exists and equals .
- BThe limit does not exist because
- CThe limit exists and equals .
- DThe limit exists and equals.

**Q8: **

Determine , where

**Q9: **

Given that determine .

- A
- B2
- C
- D

**Q10: **

Describe the limit as for the following function:

- AThe limit exists and equals .
- BThe limit exists and equals .
- CThe limit exists and equals .
- DThe limit does not exist because .
- EThe limit exists and equals .

**Q11: **

Suppose that What can be said about the existence of ?

- A The limit exists and equals 1.
- B The limit does not exist because .
- C The limit exists and equals 0.
- D The limit exists and equals .

**Q12: **

Given that find .

- A
- B5
- C
- D1

**Q13: **

Suppose that What can be said about the existence of .

- A The limit exists and equals 2.
- B The limit does not exist because .
- C The limit exists and equals .
- D The limit exists and equals 10.

**Q14: **

Discuss the existence of given .

- A The limit does not exist because .
- B The limit exists and equals .
- C The limit does not exist because does not exist.
- D The limit exists and equals .
- E The limit does not exist because does not exist.

**Q15: **

Given that find .

**Q16: **

Discuss the existence of given

- AThe limit exists and equals .
- BThe limit exists and equals .
- CThe limit does not exist because does not exist.
- DThe limit does not exist because .
- EThe limit does not exist because does not exist.

**Q17: **

Find given

- A10
- B28
- C

**Q18: **

Discuss the existence of given

- A does not exist because exist, but does not exist.
- B does not exist because .
- C does not exist because exist, but does not exist.
- D exist and equals 3.

**Q19: **

Suppose that What can be said about the existence of ?

- AThe limit exists and equals .
- BThe limit does not exist because .
- CThe limit exists and equals .

**Q20: **

Given that and exists, determine the possible values of .

- A
- B
- C
- D

**Q21: **

Given that the function has a limit when , determine the values of and .

- A ,
- B ,
- C ,
- D ,

**Q22: **

Given that find , if it exists.

- A
- B1
- C
- Ddoes not exist
- E

**Q23: **

Discuss the existence of given

- AThe limit exists and equals .
- BThe limit exists and equals .
- CThe limit does not exist because .
- DThe limit exists and equals 1.

**Q24: **

Discuss the existence of given

- AThe limit exists and equals .
- BThe limit exists and equals .
- CThe limit exists and equals .
- DThe limit does not exist because .

**Q25: **

Discuss the existence of given

- AThe limit exists and equals 9.
- BThe limit exists and equals 0.
- CThe limit exists and equals .
- DThe limit does not exist.