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
xy36x = 36

Find the limit L = limx→36 (√x − 6)/(x − 36).

f(x) = (√x − 6)/(x − 36)x → 36
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→∞ (1 + 3/x)2x. Give a decimal value.

f(x) = (1 + 3/x)2xx → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (6x3 − 6x − 5)/(5x3 + x + 9).

f(x) = (6x3 − 6x − 5)/(5x3 + x + 9)x → ∞
L =
5.Hard
xyx = 0

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

f(x) = (1 − cos 2x)/(x²)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 = 0.08333
  2. 2. L = 4
  3. 3. L = 403.4
  4. 4. L = 1.2
  5. 5. L = 2
  6. 6. L = 1.125

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