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 = 4

Find the limit L = limx→4 (x2 − 16)/(x − 4).

f(x) = (x2 − 16)/(x − 4)x → 4
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→∞ (1 − 1/x)2x. Give a decimal value.

f(x) = (1 − 1/x)2xx → ∞
L =
4.Medium
xyy = L

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

f(x) = (1 + 2/x)2xx → ∞
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 3x)/(4x²), with x in radians.

f(x) = (1 − cos 3x)/(4x²)x → 0
L =

Answer key

  1. 1. L = 8
  2. 2. L = 3
  3. 3. L = 0.1353
  4. 4. L = 54.6
  5. 5. L = 4.167
  6. 6. L = 1.125

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