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Worksheet: Limits by Algebraic Simplification

Q1:

Given that , what is ?

  • A
  • B36
  • C
  • D

Q2:

Find .

  • AThe limit doesn’t exist.
  • B
  • C
  • D

Q3:

Find .

  • AThe limit doesn’t exist.
  • B
  • C
  • D
  • E

Q4:

Find .

Q5:

Find .

  • A3
  • B
  • C
  • DThe limit doesn’t exist.

Q6:

Find .

  • A
  • B
  • C
  • D0
  • E6

Q7:

Find .

  • A
  • B
  • C
  • D0
  • E

Q8:

Find .

Q9:

Find .

  • A
  • B
  • C
  • D

Q10:

Find .

  • A
  • B
  • C
  • D0

Q11:

If , determine the values of and .

  • A,
  • B,
  • C,
  • D,

Q12:

Given that determine .

  • A
  • B
  • C5
  • D

Q13:

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

  • A
  • B2
  • C
  • D

Q14:

Suppose that What can be said about the existence of ?

  • AThe limit exists and equals 13.
  • BThe limit exists and equals 15.
  • CThe limit does not exist because .

Q15:

Given the function , what is true of ?

  • AThe limit exists and equals 40.
  • BThe limit exists and equals .
  • CThe limit does not exist because .

Q16:

Determine .

  • A5
  • B
  • C
  • D

Q17:

Given that , determine .

Q18:

Given the function , what is true of ?

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

Q19:

Determine .

  • AThe limit does not exist.
  • B28
  • C29
  • D
  • E1

Q20:

If , where determine the values of and .

  • A,
  • B,
  • C,
  • D,
  • E,

Q21:

Determine .

  • A
  • B
  • C
  • D26

Q22:

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

  • A,
  • B,
  • C,
  • D,