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 = −5

Find the limit L = limx→−5 (x2 + 2x − 15)/(x + 5).

f(x) = (x2 + 2x − 15)/(x + 5)x → −5
L =
2.Easy
xy4x = 4

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

f(x) = (√x − 2)/(x − 4)x → 4
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→∞ (√(x2 − 9x) − x).

f(x) = √(x2 − 9x) − xx → ∞
L =
5.Hard
xyx = 0

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

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

Answer key

  1. 1. L = −8
  2. 2. L = 0.25
  3. 3. L = 7.389
  4. 4. L = −4.5
  5. 5. L = 0.5
  6. 6. L = 0.125

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