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
xy16x = 16

Find the limit L = limx→16 (√x − 4)/(x − 16).

f(x) = (√x − 4)/(x − 16)x → 16
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (x3 + 2x − 7)/(2x3 + 5x + 4).

f(x) = (x3 + 2x − 7)/(2x3 + 5x + 4)x → ∞
L =
4.Medium
xyy = L

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

f(x) = (6x2 − 3x − 6)/(4x2 + 4x + 5)x → ∞
L =
5.Hard
xyx = 0

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

f(x) = (e3x − 1 − 3x)/x²x → 0
L =
6.Hard
xyx = 0

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

f(x) = (1 − cos 2x)/(3x²)x → 0
L =

Answer key

  1. 1. L = 12
  2. 2. L = 0.125
  3. 3. L = 0.5
  4. 4. L = 1.5
  5. 5. L = 4.5
  6. 6. L = 0.6667

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