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 = −1

Find the limit L = limx→−1 (x4 − 1)/(x + 1).

f(x) = (x4 − 1)/(x + 1)x → −1
L =
2.Easy
xyx = −2

Find the limit L = limx→−2 (x3 + 8)/(x + 2).

f(x) = (x3 + 8)/(x + 2)x → −2
L =
3.Medium
xyy = L

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

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

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

f(x) = (1 + 3/x)2xx → ∞
L =
5.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 =
6.Hard
xyx = 0

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

f(x) = (e−x − 1 + x)/x²x → 0
L =

Answer key

  1. 1. L = −4
  2. 2. L = 12
  3. 3. L = 0.5
  4. 4. L = 403.4
  5. 5. L = 12.5
  6. 6. L = 0.5

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