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
xy9x = 9

Find the limit L = limx→9 (√x − 3)/(x − 9).

f(x) = (√x − 3)/(x − 9)x → 9
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→∞ (√(x2 − 4x) − x).

f(x) = √(x2 − 4x) − xx → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 (e−0.5x − 1 + 0.5x)/x².

f(x) = (e−0.5x − 1 + 0.5x)/x²x → 0
L =
6.Hard
xyx = 0

Find the limit L = limx→0 (e0.5x − 1 − 0.5x)/x².

f(x) = (e0.5x − 1 − 0.5x)/x²x → 0
L =

Answer key

  1. 1. L = 0.25
  2. 2. L = 0.1667
  3. 3. L = 7.389
  4. 4. L = −2
  5. 5. L = 0.125
  6. 6. L = 0.125

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