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 (x4 − 16)/(x − 2).

f(x) = (x4 − 16)/(x − 2)x → 2
L =
2.Easy
xyx = 2

Find the limit L = limx→2 (x3 − 8)/(x − 2).

f(x) = (x3 − 8)/(x − 2)x → 2
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (−4x2 − 3x − 3)/(x2 + 2x + 5).

f(x) = (−4x2 − 3x − 3)/(x2 + 2x + 5)x → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (1 − 1/x)2x. Give a decimal value.

f(x) = (1 − 1/x)2xx → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 ln(1 + 2x)/sin(3x), with x in radians.

f(x) = ln(1 + 2x)/sin(3x)x → 0
L =
6.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 =

Answer key

  1. 1. L = 32
  2. 2. L = 12
  3. 3. L = −4
  4. 4. L = 0.1353
  5. 5. L = 0.6667
  6. 6. L = 4.167

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