# 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 .
- C would make continuous at .
- DThe function cannot be made continuous at because .

**Q3: **

Suppose What can be said of the continuity of at ?

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

**Q5: **

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

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

**Q6: **

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

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

**Q7: **

Discuss the continuity of the function at given

- A The function is continuous at .
- B The function is discontinuous at because .
- 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 .

- A2
- B
- C
- D3

**Q10: **

Consider the function

What is ?

What is ?

What is ?

What type of discontinuity does the function have at ?

- AThe function has a removable discontinuity at .
- BThe function has an essential discontinuity at .
- CThe function does not have a discontinuity at .
- DThe function has a jump discontinuity at .

**Q11: **

Consider the function

What is ?

What is ?

- AThe limit does not exist.
- B
- C
- D0
- E1

What is ?

- A1
- B0
- C
- DThe limit does not exist.
- E

What type of discontinuity does the function have at ?

- AThe function has an essential discontinuity at .
- BThe function has a removable discontinuity at .
- CThe function has a jump discontinuity at .
- DThe function does not have a discontinuity at .

**Q12: **

Determine the value of that makes continuous at , given

- A
- B
- C
- D
- E

**Q13: **

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 continuous at .
- DThe function is discontinuous at because .

**Q14: **

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

- A
- B
- C
- D

**Q15: **

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

- A
- B
- C2
- D

**Q16: **

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

- A
- B
- C
- D

**Q17: **

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 .
- EThe function is discontinuous on .

**Q18: **

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

- A
- B
- C
- D

**Q19: **

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

- A2
- B
- C
- D
- E

**Q20: **

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 .

**Q21: **

Let Find all values of that make continuous at .

- A
- B
- C
- D

**Q22: **

Let Find all values of that make continuous at .

- A
- B0
- C
- D

**Q23: **

Suppose What can be said of the continuity of at ?

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

**Q24: **

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

- A4
- B
- C
- D
- E