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 = 5

Find the limit L = limx→5 (x2 + x − 30)/(x − 5).

f(x) = (x2 + x − 30)/(x − 5)x → 5
L =
2.Easy
xyx = −2

Find the limit L = limx→−2 (x4 − 16)/(x + 2).

f(x) = (x4 − 16)/(x + 2)x → −2
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (−2x2 − 3x − 4)/(4x2 + 4x + 2).

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

Find the limit L = limx→∞ (1 + 0.5/x)2x. Give a decimal value.

f(x) = (1 + 0.5/x)2xx → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 ln(1 + 5x)/sin(3x), with x in radians.

f(x) = ln(1 + 5x)/sin(3x)x → 0
L =
6.Hard
xyx = 0

Find the limit L = limx→0 (1 − cos 5x)/(2x²), with x in radians.

f(x) = (1 − cos 5x)/(2x²)x → 0
L =

Answer key

  1. 1. L = 11
  2. 2. L = −32
  3. 3. L = −0.5
  4. 4. L = 2.718
  5. 5. L = 1.667
  6. 6. L = 6.25

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