# Worksheet: Continuity at a Point

In this worksheet, we will practice checking the continuity of a function at a given point.

**Q2: **

Given If possible or necessary, define so that is continuous at .

- A would make continuous at .
- BThe function is already continuous at .
- CThe function cannot be made continuous at because .
- D would make continuous at .

**Q3: **

Suppose What can be said of the continuity of at ?

- A The function is continuous on .
- B The function is discontinuous at because .
- C The function is discontinuous at because does not exist.
- D The function is discontinuous at because is undefined.
- E The function is continuous at .

**Q5: **

Given , if possible or necessary, define so that is continuous at .

- A makes continuous at .
- BThe function cannot be made continuous at because is undefined.
- CThe function is already continuous at .
- DNo value of will make continuous because does not exist.

**Q6: **

Given , if possible or necessary, define so that is continuous at .

- ANo value of will make continuous because does not exist.
- BThe function cannot be made continuous at because is undefined.
- CThe function is already continuous at .
- D makes continuous at .

**Q7: **

Discuss the continuity of the function at given

- A The function is discontinuous at because .
- B The function is continuous at .
- C The function is discontinuous at because is undefined.
- D The function is discontinuous at because does not exist.

**Q8: **

Find the value of that makes continuous at , given that

**Q9: **

Setting and when makes continuous at . Determine .

- A
- B2
- C3
- D

**Q10: **

Determine the value of that makes continuous at , given

- A
- B
- C
- D
- E

**Q11: **

Discuss the continuity of the function at , given

- AThe function is discontinuous at because is undefined.
- BThe function is discontinuous at because .
- CThe function is discontinuous at because does not exist.
- DThe function is continuous at .

**Q12: **

The function is continuous at . Determine the possible values of .

- A
- B
- C
- D

**Q13: **

Determine the value of that makes the function continuous at , given

- A2
- B
- C
- D

**Q14: **

Find the value of that makes the function continuous at , given that

- A
- B
- C
- D

**Q15: **

Discuss the continuity of the function at , given

- AThe function is discontinuous on .
- BThe function is discontinuous at because is undefined.
- CThe function is discontinuous at because does not exist.
- DThe function is continuous at .
- EThe function is discontinuous at because .

**Q16: **

Determine the value of that makes the function continuous at , given that

- A9
- B30
- C24
- D198

**Q17: **

Find the value of which makes the function continuous at , given that

- A2
- B
- C
- D
- E

**Q18: **

Discuss the continuity of the function at , given

- AThe function is discontinuous at because is undefined.
- BThe function is discontinuous at because does not exist.
- CThe function is continuous at .
- DThe function is discontinuous at because .

**Q19: **

Let Find all values of that make continuous at .

- A
- B
- C
- D

**Q20: **

Let Find all values of that make continuous at .

- A
- B
- C
- D0

**Q21: **

Suppose What can be said of the continuity of at ?

- A The function is discontinuous at because does not exist.
- B The function is discontinuous at because .
- C The function is continuous at .
- D The function is discontinuous at because is undefined.
- E The function is continuous on .

**Q22: **

Find the value of which makes the function continuous at , given

- A4
- B
- C
- D
- E

**Q23: **

Discuss the continuity of the function at , given that

- A The function is continuous at all points in .
- B The function is discontinuous at because .
- C The function is continuous at .
- D The function is discontinuous at because does not exist.
- E The function is discontinuous at because is undefined.

**Q24: **

Discuss the continuity of the function at , given that

- A The function is continuous at .
- B The function is continuous on .
- C The function is discontinuous at because does not exist.
- D The function is discontinuous at because .
- E The function is discontinuous at because is undefined.

**Q25: **

Discuss the continuity of the function at , given that

- AThe function is continuous at .
- BThe function is discontinuous on .
- CThe function is discontinuous at because is undefined.
- DThe function is discontinuous at because does not exist.
- EThe function is discontinuous at because .