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 (x3 − 1)/(x − 1).

f(x) = (x3 − 1)/(x − 1)x → 1
L =
2.Easy
xyx = 4

Find the limit L = limx→4 (x2 − 2x − 8)/(x − 4).

f(x) = (x2 − 2x − 8)/(x − 4)x → 4
L =
3.Medium
xyy = L

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

f(x) = √(x2 − 10x) − xx → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (−3x2 + x + 5)/(3x2 + x + 2).

f(x) = (−3x2 + x + 5)/(3x2 + x + 2)x → ∞
L =
5.Hard
xyx = 0

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

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

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

f(x) = ln(1 + 4x)/sin(3x)x → 0
L =

Answer key

  1. 1. L = 3
  2. 2. L = 6
  3. 3. L = −5
  4. 4. L = −1
  5. 5. L = 4.5
  6. 6. L = 1.333

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