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 (x3 − 8)/(x − 2).

f(x) = (x3 − 8)/(x − 2)x → 2
L =
2.Easy
xyx = 0

Find the limit L = limx→0 (x2 − 3x)/(x).

f(x) = (x2 − 3x)/(x)x → 0
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (6x2 − x + 3)/(4x2 + 5x + 3).

f(x) = (6x2 − x + 3)/(4x2 + 5x + 3)x → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (√(4x2 − 3x) − 2x).

f(x) = √(4x2 − 3x) − 2xx → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 (1 − cos 3x)/(2x²), with x in radians.

f(x) = (1 − cos 3x)/(2x²)x → 0
L =
6.Hard
xyx = 0

Find the limit L = limx→0 (e3x − 1 − 3x)/x².

f(x) = (e3x − 1 − 3x)/x²x → 0
L =

Answer key

  1. 1. L = 12
  2. 2. L = −3
  3. 3. L = 1.5
  4. 4. L = −0.75
  5. 5. L = 2.25
  6. 6. L = 4.5

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