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 = 5

Find the limit L = limx→5 (x2 − x − 20)/(x − 5).

f(x) = (x2 − x − 20)/(x − 5)x → 5
L =
2.Easy
xyx = −2

Find the limit L = limx→−2 (x2 − 2x − 8)/(x + 2).

f(x) = (x2 − 2x − 8)/(x + 2)x → −2
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (2x3 − 5x + 8)/(x3 + x + 2).

f(x) = (2x3 − 5x + 8)/(x3 + x + 2)x → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (−5x2 + x + 2)/(x2 + x + 9).

f(x) = (−5x2 + x + 2)/(x2 + x + 9)x → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 ln(1 + 3x)/sin(4x), with x in radians.

f(x) = ln(1 + 3x)/sin(4x)x → 0
L =
6.Hard
xyx = 0

Find the limit L = limx→0 (e0.5x − 1 − 0.5x)/x².

f(x) = (e0.5x − 1 − 0.5x)/x²x → 0
L =

Answer key

  1. 1. L = 9
  2. 2. L = −6
  3. 3. L = 2
  4. 4. L = −5
  5. 5. L = 0.75
  6. 6. L = 0.125

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