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 (x3 + 27)/(x + 3).

f(x) = (x3 + 27)/(x + 3)x → −3
L =
2.Easy
xyx = 5

Find the limit L = limx→5 (x2 − 9x + 20)/(x − 5).

f(x) = (x2 − 9x + 20)/(x − 5)x → 5
L =
3.Medium
xyy = L

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

f(x) = (1 − 1/x)2xx → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (−2x2 − x − 5)/(5x2 + 3x + 8).

f(x) = (−2x2 − x − 5)/(5x2 + 3x + 8)x → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 ln(1 + 3x)/sin(4x), with x in radians.

f(x) = ln(1 + 3x)/sin(4x)x → 0
L =
6.Hard
xyx = 0

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

f(x) = (1 − cos 5x)/(x²)x → 0
L =

Answer key

  1. 1. L = 27
  2. 2. L = 1
  3. 3. L = 0.1353
  4. 4. L = −0.4
  5. 5. L = 0.75
  6. 6. L = 12.5

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