Limits worksheet with answers

Free printable Limits worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
xyx = 3

Find the limit L = limx→3 (x2 + 3x − 18)/(x − 3).

f(x) = (x2 + 3x − 18)/(x − 3)x → 3
L =
2.Easy
xyx = −4

Find the limit L = limx→−4 (x2 − 2x − 24)/(x + 4).

f(x) = (x2 − 2x − 24)/(x + 4)x → −4
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (√(4x2 + 2x) − 2x).

f(x) = √(4x2 + 2x) − 2xx → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (√(4x2 − 7x) − 2x).

f(x) = √(4x2 − 7x) − 2xx → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 (1 − cos 2x)/(4x²), with x in radians.

f(x) = (1 − cos 2x)/(4x²)x → 0
L =
6.Hard
xyx = 0

Find the limit L = limx→0 (1 − cos 3x)/(2x²), with x in radians.

f(x) = (1 − cos 3x)/(2x²)x → 0
L =

Answer key

  1. 1. L = 9
  2. 2. L = −10
  3. 3. L = 0.5
  4. 4. L = −1.75
  5. 5. L = 0.5
  6. 6. L = 2.25

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