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
xy36x = 36

Find the limit L = limx→36 (√x − 6)/(x − 36).

f(x) = (√x − 6)/(x − 36)x → 36
L =
3.Medium
xyy = L

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

f(x) = (1 + 0.5/x)xx → ∞
L =
4.Medium
xyy = L

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

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

Find the limit L = limx→0 ln(1 + x)/sin(2x), with x in radians.

f(x) = ln(1 + x)/sin(2x)x → 0
L =
6.Hard
xyx = 0

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

f(x) = ln(1 + 3x)/sin(5x)x → 0
L =

Answer key

  1. 1. L = 27
  2. 2. L = 0.08333
  3. 3. L = 1.649
  4. 4. L = 54.6
  5. 5. L = 0.5
  6. 6. L = 0.6

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