# Lesson Worksheet: Continuity and Limits Mathematics

In this worksheet, we will practice checking the continuity of a function at a given point by using limits and using the mean value theorem on continuous functions.

**Q1: **

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

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

**Q2: **

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

- A will make continuous at .
- B is already continuous on .
- CThe function is already continuous at .
- D will make continuous at .
- EThe function cannot be made continuous at by defining as does not exist.

**Q3: **

Find the values of and that make the function continuous at and at , given

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

**Q4: **

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

- A
- B
- C
- D
- E

**Q5: **

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

- AThe function cannot be made continuous at because does not exist.
- BSetting makes continuous at .
- CThe function cannot be made continuous at because is undefined.
- DThe function is already continuous at

**Q6: **

Find the values of which make the function continuous at if

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

**Q7: **

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

**Q8: **

Setting and when makes continuous at . Determine .

- A
- B3
- C
- D2

**Q9: **

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 .

**Q10: **

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

- AThe function is already continuous at .
- B would make continuous at .
- C would make continuous at .
- DThe function cannot be made continuous at because .