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 = −1

Find the limit L = limx→−1 (x3 + 1)/(x + 1).

f(x) = (x3 + 1)/(x + 1)x → −1
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (√(9x2 + 2x) − 3x).

f(x) = √(9x2 + 2x) − 3xx → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (√(x2 − 4x) − x).

f(x) = √(x2 − 4x) − xx → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 (1 − cos 5x)/(3x²), with x in radians.

f(x) = (1 − cos 5x)/(3x²)x → 0
L =
6.Hard
xyx = 0

Find the limit L = limx→0 (1 − cos 5x)/(4x²), with x in radians.

f(x) = (1 − cos 5x)/(4x²)x → 0
L =

Answer key

  1. 1. L = 3
  2. 2. L = 3
  3. 3. L = 0.3333
  4. 4. L = −2
  5. 5. L = 4.167
  6. 6. L = 3.125

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