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 = 3

Find the limit L = limx→3 (x2 + x − 12)/(x − 3).

f(x) = (x2 + x − 12)/(x − 3)x → 3
L =
2.Easy
xy25x = 25

Find the limit L = limx→25 (√x − 5)/(x − 25).

f(x) = (√x − 5)/(x − 25)x → 25
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (2x2 − 2x + 8)/(x2 + x + 2).

f(x) = (2x2 − 2x + 8)/(x2 + x + 2)x → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (6x2 − x + 4)/(x2 + x + 4).

f(x) = (6x2 − x + 4)/(x2 + x + 4)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 + 3x)/sin(2x), with x in radians.

f(x) = ln(1 + 3x)/sin(2x)x → 0
L =

Answer key

  1. 1. L = 7
  2. 2. L = 0.1
  3. 3. L = 2
  4. 4. L = 6
  5. 5. L = 2
  6. 6. L = 1.5

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