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 − 30)/(x − 5).

f(x) = (x2 + x − 30)/(x − 5)x → 5
L =
2.Easy
xyx = 1

Find the limit L = limx→1 (x2 + x − 2)/(x − 1).

f(x) = (x2 + x − 2)/(x − 1)x → 1
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (−5x2 + 6x − 9)/(4x2 + x + 8).

f(x) = (−5x2 + 6x − 9)/(4x2 + x + 8)x → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (√(9x2 + 10x) − 3x).

f(x) = √(9x2 + 10x) − 3xx → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 (1 − cos 4x)/(3x²), with x in radians.

f(x) = (1 − cos 4x)/(3x²)x → 0
L =
6.Hard
xyx = 0

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

f(x) = ln(1 + x)/sin(4x)x → 0
L =

Answer key

  1. 1. L = 11
  2. 2. L = 3
  3. 3. L = −1.25
  4. 4. L = 1.667
  5. 5. L = 2.667
  6. 6. L = 0.25

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