# 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 .