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
xy4x = 4

Find the limit L = limx→4 (√x − 2)/(x − 4).

f(x) = (√x − 2)/(x − 4)x → 4
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (1 + 2/x)3x. Give a decimal value.

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

Find the limit L = limx→∞ (−2x2 + 5)/(2x2 + x + 4).

f(x) = (−2x2 + 5)/(2x2 + x + 4)x → ∞
L =
5.Hard
xyx = 0

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

f(x) = (e−2x − 1 + 2x)/x²x → 0
L =
6.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 =

Answer key

  1. 1. L = 27
  2. 2. L = 0.25
  3. 3. L = 403.4
  4. 4. L = −1
  5. 5. L = 2
  6. 6. L = 2.667

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