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
xy4x = 4

Find the limit L = limx→4 (√x − 2)/(x − 4).

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

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

Find the limit L = limx→0 (e−2x − 1 + 2x)/x².

f(x) = (e−2x − 1 + 2x)/x²x → 0
L =
6.Hard
xyx = 0

Find the limit L = limx→0 ln(1 + 5x)/sin(3x), with x in radians.

f(x) = ln(1 + 5x)/sin(3x)x → 0
L =

Answer key

  1. 1. L = 0.25
  2. 2. L = 12
  3. 3. L = 7.389
  4. 4. L = 0.3679
  5. 5. L = 2
  6. 6. L = 1.667

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