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 = 2

Find the limit L = limx→2 (x4 − 16)/(x − 2).

f(x) = (x4 − 16)/(x − 2)x → 2
L =
2.Easy
xy36x = 36

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

f(x) = (√x − 6)/(x − 36)x → 36
L =
3.Medium
xyy = L

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

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

Find the limit L = limx→∞ (−6x2 − 3x − 6)/(3x2 + x + 8).

f(x) = (−6x2 − 3x − 6)/(3x2 + x + 8)x → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 ln(1 + 5x)/sin(3x), with x in radians.

f(x) = ln(1 + 5x)/sin(3x)x → 0
L =
6.Hard
xyx = 0

Find the limit L = limx→0 ln(1 + x)/sin(4x), with x in radians.

f(x) = ln(1 + x)/sin(4x)x → 0
L =

Answer key

  1. 1. L = 32
  2. 2. L = 0.08333
  3. 3. L = 2.718
  4. 4. L = −2
  5. 5. L = 1.667
  6. 6. L = 0.25

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