Lesson Worksheet: Continuity at a Point Mathematics • 12th Grade
In this worksheet, we will practice checking the continuity of a function at a given point.
Q1:
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 .
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:
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.
Q4:
Find the values of which make the function continuous at if
- A,
- B,
- C,
- D,
- E,
Q5:
Is continuous at ?
- AYes
- BNo
Q6:
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
Q7:
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 .
Q8:
Find the value of which makes the function continuous at , given
- A
- B
- C
- D
- E
Q9:
Find the values of and that make the function continuous at and at , given
- A,
- B,
- C,
- D,
Q10:
Find the values of and that make the function continuous at and , given that
- A,
- B,
- C,
- D,
- E,