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→∞ (−5x3 − 5x + 1)/(x3 + x + 7).

f(x) = (−5x3 − 5x + 1)/(x3 + x + 7)x → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (−3x3 − x − 1)/(2x3 + 4x + 9).

f(x) = (−3x3 − x − 1)/(2x3 + 4x + 9)x → ∞
L =
5.Hard
xyx = 0

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

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

Find the limit L = limx→0 (1 − cos 5x)/(2x²), with x in radians.

f(x) = (1 − cos 5x)/(2x²)x → 0
L =

Answer key

  1. 1. L = −4
  2. 2. L = 12
  3. 3. L = −5
  4. 4. L = −1.5
  5. 5. L = 0.5
  6. 6. L = 6.25

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