Worksheet: Limits by Rationalization

In this worksheet, we will practice evaluating limits for radical functions at a point by rationalizing the denominator, the numerator, or both.

Q1:

Find l i m 𝑥 4 2 2 2 2 𝑥 1 6 + 4 4 𝑥 1 6 𝑥 1 2 𝑥 1 6 4 .

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

Q2:

By rationalizing and using limit laws, determine l i m 𝑛 + 3 𝑛 𝑛 .

  • A3
  • B 1 2
  • C6
  • D 3 2
  • E2

Q3:

Find l i m 𝑥 2 2 2 2 3 𝑥 + 3 7 + 7 3 𝑥 6 𝑥 2 3 𝑥 + 3 7 7 .

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

Q4:

Find l i m 𝑥 2 2 2 2 3 𝑥 + 1 3 + 5 2 𝑥 4 𝑥 3 3 𝑥 + 1 3 5 .

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

Q5:

Find l i m 𝑥 7 2 2 2 𝑥 + 3 2 + 9 2 𝑥 1 4 𝑥 1 𝑥 + 3 2 9 .

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

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