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 = 1

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

f(x) = (x4 − 1)/(x − 1)x → 1
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→∞ (√(x2 − 8x) − x).

f(x) = √(x2 − 8x) − xx → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (−x3 − 4x + 5)/(3x3 + 3x + 7).

f(x) = (−x3 − 4x + 5)/(3x3 + 3x + 7)x → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 (e2x − 1 − 2x)/x².

f(x) = (e2x − 1 − 2x)/x²x → 0
L =
6.Hard
xyx = 0

Find the limit L = limx→0 ln(1 + 4x)/sin(2x), with x in radians.

f(x) = ln(1 + 4x)/sin(2x)x → 0
L =

Answer key

  1. 1. L = 4
  2. 2. L = 0.08333
  3. 3. L = −4
  4. 4. L = −0.3333
  5. 5. L = 2
  6. 6. L = 2

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