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 (x4 − 16)/(x + 2).

f(x) = (x4 − 16)/(x + 2)x → −2
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→∞ (√(x2 + 3x) − x).

f(x) = √(x2 + 3x) − xx → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (4x2 + x + 8)/(3x2 + 3x + 3).

f(x) = (4x2 + x + 8)/(3x2 + 3x + 3)x → ∞
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 ln(1 + 4x)/sin(2x), with x in radians.

f(x) = ln(1 + 4x)/sin(2x)x → 0
L =

Answer key

  1. 1. L = −32
  2. 2. L = 12
  3. 3. L = 1.5
  4. 4. L = 1.333
  5. 5. L = 12.5
  6. 6. L = 2

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