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
xy9x = 9

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

f(x) = (√x − 3)/(x − 9)x → 9
L =
2.Easy
xyx = 1

Find the limit L = limx→1 (x4 − 1)/(x − 1).

f(x) = (x4 − 1)/(x − 1)x → 1
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (√(x2 + 5x) − x).

f(x) = √(x2 + 5x) − xx → ∞
L =
4.Medium
xyy = L

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

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

Find the limit L = limx→0 ln(1 + 2x)/sin(5x), with x in radians.

f(x) = ln(1 + 2x)/sin(5x)x → 0
L =
6.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 =

Answer key

  1. 1. L = 0.1667
  2. 2. L = 4
  3. 3. L = 2.5
  4. 4. L = 20.09
  5. 5. L = 0.4
  6. 6. L = 5

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