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Worksheet: Limits by Algebraic Simplification

Q1:

Given that , what is ?

  • A
  • B
  • C
  • D36

Q2:

Find .

  • A
  • B
  • CThe limit doesn’t exist.
  • D

Q3:

Find .

  • A
  • B
  • C
  • D
  • EThe limit doesn’t exist.

Q4:

Find .

Q5:

Find .

  • A
  • BThe limit doesn’t exist.
  • C3
  • D

Q6:

Find .

  • A0
  • B6
  • C
  • D
  • E

Q7:

Find .

  • A0
  • B
  • C
  • D
  • E

Q8:

Find .

Q9:

Find .

  • A
  • B
  • C
  • D

Q10:

Find .

  • A
  • B0
  • C
  • D

Q11:

If , determine the values of and .

  • A ,
  • B ,
  • C ,
  • D ,

Q12:

Given that determine .

  • A5
  • B
  • C
  • D

Q13:

Given that the limit of the function exists when , determine the value of .

  • A
  • B
  • C
  • D2

Q14:

Suppose that What can be said about the existence of ?

  • A The limit exists and equals 15.
  • B The limit does not exist because .
  • C The limit exists and equals 13.

Q15:

Given the function , what is true of ?

  • A The limit exists and equals .
  • B The limit does not exist because .
  • C The limit exists and equals 40.

Q16:

Determine .

  • A
  • B
  • C5
  • D

Q17:

Given that , determine .

Q18:

Given the function , what is true of ?

  • AThe limit exists and equals 45.
  • BThe limit exists and equals .
  • CThe limit exists and equals 15.
  • DThe limit does not exist because .
  • EThe limit exists and equals .

Q19:

Determine .

  • A
  • B1
  • C28
  • D29
  • EThe limit does not exist.

Q20:

If , where determine the values of and .

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q21:

Determine .

  • A
  • B26
  • C
  • D

Q22:

The function has a limit at and . What are the values of and ?

  • A ,
  • B ,
  • C ,
  • D ,