# Lesson Worksheet: Continuity at a Point Mathematics • Higher Education

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

**Q3: **

Suppose What can be said of the continuity of at ?

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

**Q6: **

Discuss the continuity of the function at given

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

**Q7: **

Find the value of that makes continuous at , given that

**Q8: **

Setting and when makes continuous at . Determine .

- A
- B3
- C
- D2

**Q9: **

Determine the value of that makes continuous at , given

- A
- B
- C
- D
- E

**Q10: **

Discuss the continuity of the function at , given

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

**Q11: **

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

- A
- B
- C
- D

**Q12: **

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

- A
- B
- C2
- D

**Q13: **

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

- A
- B
- C
- D

**Q14: **

Discuss the continuity of the function at , given

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

**Q15: **

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

- A30
- B198
- C24
- D9

**Q17: **

Let Find all values of that make continuous at .

- A
- B
- C
- D

**Q18: **

Let Find all values of that make continuous at .

- A
- B0
- C
- D

**Q19: **

Discuss the continuity of the function at , given that

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

**Q20: **

Discuss the continuity of the function at , given that

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

**Q22: **

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

- AThe function cannot be made continuous at because is undefined.
- B makes continuous at .
- CNo value of will make continuous because does not exist.
- DThe function is already continuous at .

**Q23: **

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 .

**Q24: **

Suppose What can be said of the continuity of at ?

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

**Q25: **

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

- A would make continuous at .
- B would make continuous at .
- CThe function can not be made continuous at because does not exist.
- DThe function is already continuous at .