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Worksheet: Limits by Simplifying Complex Fractions

Q1:

Find l i m π‘₯ β†’ 2 2 2 2 ο€Ύ π‘₯ π‘₯ βˆ’ 4 + π‘₯ βˆ’ 6 π‘₯ βˆ’ 4  .

  • A βˆ’ 6
  • B0
  • C 1 4
  • D 5 4

Q2:

Find l i m π‘₯ β†’ 2 2 2 ο€Ύ π‘₯ βˆ’ 4 π‘₯ βˆ’ 9 Γ— π‘₯ βˆ’ 3 π‘₯ βˆ’ 2  .

  • A 2 5
  • B 8 5
  • CThe limit doesn’t exist.
  • D 4 5

Q3:

Determine l i m  β†’         βˆ’ π‘₯ βˆ’ 4 .

  • A βˆ’ 1 3 2 0
  • B βˆ’ 5 1 2 8
  • C 1 1 2 8
  • D βˆ’ 5 2 5 6
  • EThe limit does not exist.

Q4:

Determine l i m π‘₯ β†’ βˆ’ 5 1 π‘₯ + 7 1 7 βˆ’ π‘₯ .

  • A βˆ’ 1 2
  • B βˆ’ 1 7
  • C 5 1 4
  • D βˆ’ 1 1 4

Q5:

Determine l i m π‘₯ β†’ 4 3 ο€Ό 1 π‘₯ βˆ’ 4 βˆ’ 4 8 π‘₯ βˆ’ 6 4  .

  • A4
  • B 1 1 6
  • C2
  • D 1 4
  • EThe limit does not exist.

Q6:

Find l i m π‘₯ β†’ 0 1 π‘₯ + 6 1 6 βˆ’ π‘₯ .

  • A βˆ’ 1 1 2
  • B βˆ’ 1 6
  • CThe limit does not exist.
  • D βˆ’ 1 3 6

Q7:

Find l i m π‘₯ β†’ 1 5 1 π‘₯ 1 π‘₯ π‘₯ βˆ’ π‘₯ βˆ’ 5 .

  • A0
  • B βˆ’ 5
  • C1
  • D5
  • E βˆ’ 1

Q8:

Find l i m π‘₯ β†’ βˆ’ 1 2 7 3 ο€Ύ π‘₯ βˆ’ 5 π‘₯ βˆ’ 6 π‘₯ + 1 + π‘₯ + 1 π‘₯ + 1  .

  • A 1 7 3
  • B8
  • CThe limit does not exist.
  • D βˆ’ 1 4 3
  • E 2 2 3

Q9:

Determine l i m π‘₯ β†’ 4 2 ο€Ύ βˆ’ 5 π‘₯ + 9 π‘₯ βˆ’ 3 6 π‘₯ π‘₯ βˆ’ 4  .

  • A βˆ’ 1 4 9 4
  • B βˆ’ 5 4
  • C36
  • D 1 3 9 4
  • EThe limit does not exist.