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Worksheet: Continuity of a Function

Q1:

Find the set on which is continuous.

  • A
  • B
  • C
  • D

Q2:

Find the set on which is continuous.

  • A is continuous on .
  • B is continuous on .
  • C is continuous on .
  • D is continuous on .

Q3:

Use continuity to evaluate .

  • A3
  • B0
  • C1
  • D
  • E9

Q4:

The function is given by Determine and so that is continuous everywhere.

  • A ,
  • B ,
  • C ,
  • D ,

Q5:

Find the set on which is continuous.

  • AThe function is continuous on .
  • BThe function is continuous on .
  • CThe function is continuous on .
  • DThe function is continuous on .
  • EThe function is continuous on because and are continuous on .

Q6:

Given that and are continuous functions such that and , determine .

  • A
  • B
  • C
  • D
  • E

Q7:

Which of the following holds for ?

  • A The function is continuous on because is continuous on .
  • B The function is continuous on because is continuous on .
  • C The function is continuous on .
  • D The function is continuous on because both of and are continuous on .
  • E The function is continuous on .

Q8:

Use continuity to evaluate .

  • A
  • B
  • C
  • D
  • E8

Q9:

Use continuity to evaluate .

Q10:

Use continuity to evaluate .

  • A
  • B
  • C1
  • D0

Q11:

Given that and are continuous functions such that and , determine .

  • A
  • B
  • C
  • D
  • E

Q12:

Find the set on which is continuous.

  • A is continuous on .
  • B is continuous on .
  • C is continuous on .
  • D is continuous on .
  • E is continuous on .

Q13:

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

  • A
  • B
  • C1
  • D

Q14:

Suppose and What can be said of the continuity of at ?

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

Q15:

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 .

Q16:

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 .

Q17:

Suppose Discuss whether it is possible to define to obtain a function that is continuous at this point.

  • AThe function is continuous at .
  • BThe function can be defined to be continuous at as
  • CThe function cannot be defined to be continuous at because does not exist.
  • DThe function can be defined to be continuous at as
  • EThe function cannot be defined to be continuous at because is undefined.