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 = 0

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

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

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

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

Find the limit L = limx→∞ (1 + 3/x)x. Give a decimal value.

f(x) = (1 + 3/x)xx → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 (1 − cos 4x)/(3x²), with x in radians.

f(x) = (1 − cos 4x)/(3x²)x → 0
L =
6.Hard
xyx = 0

Find the limit L = limx→0 (e2x − 1 − 2x)/x².

f(x) = (e2x − 1 − 2x)/x²x → 0
L =

Answer key

  1. 1. L = 27
  2. 2. L = 1
  3. 3. L = 0.01832
  4. 4. L = 20.09
  5. 5. L = 2.667
  6. 6. L = 2

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