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Worksheet: Evaluating Limits Algebraically at a Point Using Rationalization

Q1:

By rationalizing and using limit laws, determine .

  • A3
  • B
  • C6
  • D
  • E2

Q2:

Find l i m π‘₯ β†’ 4 2 2 2 √ 2 π‘₯ βˆ’ 1 6 + 4 4 π‘₯ βˆ’ 1 6 π‘₯ βˆ’ 1 √ 2 π‘₯ βˆ’ 1 6 βˆ’ 4 .

  • AThe limit does not exist.
  • B4
  • C0
  • D βˆ’ 1 1 6
  • E 1 3 2

Q3:

Find l i m π‘₯ β†’ 2 2 2 2 √ 3 π‘₯ + 3 7 + 7 3 π‘₯ βˆ’ 6 π‘₯ βˆ’ 2 √ 3 π‘₯ + 3 7 βˆ’ 7 .

  • AThe limit does not exist.
  • B2
  • C0
  • D βˆ’ 7 1 2
  • E 7 3 6

Q4:

Find l i m π‘₯ β†’ 2 2 2 2 √ 3 π‘₯ + 1 3 + 5 2 π‘₯ βˆ’ 4 π‘₯ βˆ’ 3 √ 3 π‘₯ + 1 3 βˆ’ 5 .

  • AThe limit does not exist.
  • B2
  • C0
  • D βˆ’ 5 8
  • E 5 2 4

Q5:

Find l i m π‘₯ β†’ 7 2 2 2 √ π‘₯ + 3 2 + 9 2 π‘₯ βˆ’ 1 4 π‘₯ βˆ’ 1 √ π‘₯ + 3 2 βˆ’ 9 .

  • AThe limit does not exist.
  • B7
  • C0
  • D βˆ’ 9 9 8
  • E 9 9 8