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 = 2

Find the limit L = limx→2 (x2 − 8x + 12)/(x − 2).

f(x) = (x2 − 8x + 12)/(x − 2)x → 2
L =
2.Easy
xyx = 0

Find the limit L = limx→0 (x2 − 3x)/(x).

f(x) = (x2 − 3x)/(x)x → 0
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (2x2 − 5x − 3)/(x2 + 2x + 1).

f(x) = (2x2 − 5x − 3)/(x2 + 2x + 1)x → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (1 − 1/x)2x. Give a decimal value.

f(x) = (1 − 1/x)2xx → ∞
L =
5.Hard
xyx = 0

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

f(x) = (1 − cos 3x)/(x²)x → 0
L =
6.Hard
xyx = 0

Find the limit L = limx→0 (1 − cos 5x)/(4x²), with x in radians.

f(x) = (1 − cos 5x)/(4x²)x → 0
L =

Answer key

  1. 1. L = −4
  2. 2. L = −3
  3. 3. L = 2
  4. 4. L = 0.1353
  5. 5. L = 4.5
  6. 6. L = 3.125

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