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 = 3

Find the limit L = limx→3 (x3 − 27)/(x − 3).

f(x) = (x3 − 27)/(x − 3)x → 3
L =
2.Easy
xyx = −5

Find the limit L = limx→−5 (x2 + 11x + 30)/(x + 5).

f(x) = (x2 + 11x + 30)/(x + 5)x → −5
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (√(9x2 − 6x) − 3x).

f(x) = √(9x2 − 6x) − 3xx → ∞
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 ln(1 + 5x)/sin(x), with x in radians.

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

Find the limit L = limx→0 (e1.5x − 1 − 1.5x)/x².

f(x) = (e1.5x − 1 − 1.5x)/x²x → 0
L =

Answer key

  1. 1. L = 27
  2. 2. L = 1
  3. 3. L = −1
  4. 4. L = 4.482
  5. 5. L = 5
  6. 6. L = 1.125

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