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 (x2 + 7x + 6)/(x + 1).

f(x) = (x2 + 7x + 6)/(x + 1)x → −1
L =
2.Easy
xy1x = 1

Find the limit L = limx→1 (√x − 1)/(x − 1).

f(x) = (√x − 1)/(x − 1)x → 1
L =
3.Medium
xyy = L

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

f(x) = (1 + 3/x)xx → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (1 + 0.5/x)3x. Give a decimal value.

f(x) = (1 + 0.5/x)3xx → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 (1 − cos 4x)/(2x²), with x in radians.

f(x) = (1 − cos 4x)/(2x²)x → 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 = 5
  2. 2. L = 0.5
  3. 3. L = 20.09
  4. 4. L = 4.482
  5. 5. L = 4
  6. 6. L = 0.125

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