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 = −2

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

f(x) = (x3 + 8)/(x + 2)x → −2
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→∞ (−6x3 + 3x − 3)/(3x3 + 4x + 2).

f(x) = (−6x3 + 3x − 3)/(3x3 + 4x + 2)x → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (√(x2 + 10x) − x).

f(x) = √(x2 + 10x) − xx → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 (1 − cos 2x)/(3x²), with x in radians.

f(x) = (1 − cos 2x)/(3x²)x → 0
L =
6.Hard
xyx = 0

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

f(x) = (ex − 1 − x)/x²x → 0
L =

Answer key

  1. 1. L = 12
  2. 2. L = 0.25
  3. 3. L = −2
  4. 4. L = 5
  5. 5. L = 0.6667
  6. 6. L = 0.5

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