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 = −1

Find the limit L = limx→−1 (x2 + 5x + 4)/(x + 1).

f(x) = (x2 + 5x + 4)/(x + 1)x → −1
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (√(9x2 + 7x) − 3x).

f(x) = √(9x2 + 7x) − 3xx → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (5x3 − 9)/(5x3 + 6x + 3).

f(x) = (5x3 − 9)/(5x3 + 6x + 3)x → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 (1 − cos 2x)/(4x²), with x in radians.

f(x) = (1 − cos 2x)/(4x²)x → 0
L =
6.Hard
xyx = 0

Find the limit L = limx→0 ln(1 + 4x)/sin(5x), with x in radians.

f(x) = ln(1 + 4x)/sin(5x)x → 0
L =

Answer key

  1. 1. L = 4
  2. 2. L = 3
  3. 3. L = 1.167
  4. 4. L = 1
  5. 5. L = 0.5
  6. 6. L = 0.8

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