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 (x2 + x − 6)/(x − 2).

f(x) = (x2 + x − 6)/(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→∞ (4x2 + x + 1)/(3x2 + 5x + 5).

f(x) = (4x2 + x + 1)/(3x2 + 5x + 5)x → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (−4x2 − 7)/(x2 + 5x + 8).

f(x) = (−4x2 − 7)/(x2 + 5x + 8)x → ∞
L =
5.Hard
xyx = 0

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

f(x) = (ex − 1 − x)/x²x → 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 = 5
  2. 2. L = 0.08333
  3. 3. L = 1.333
  4. 4. L = −4
  5. 5. L = 0.5
  6. 6. L = 1.125

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