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 = 5

Find the limit L = limx→5 (x2 − 9x + 20)/(x − 5).

f(x) = (x2 − 9x + 20)/(x − 5)x → 5
L =
3.Medium
xyy = L

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

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

Find the limit L = limx→∞ (1 + 1/x)3x. Give a decimal value.

f(x) = (1 + 1/x)3xx → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 ln(1 + 5x)/sin(2x), with x in radians.

f(x) = ln(1 + 5x)/sin(2x)x → 0
L =
6.Hard
xyx = 0

Find the limit L = limx→0 ln(1 + 4x)/sin(5x), with x in radians.

f(x) = ln(1 + 4x)/sin(5x)x → 0
L =

Answer key

  1. 1. L = 3
  2. 2. L = 1
  3. 3. L = 7.389
  4. 4. L = 20.09
  5. 5. L = 2.5
  6. 6. L = 0.8

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