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
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→∞ (√(4x2 − 9x) − 2x).

f(x) = √(4x2 − 9x) − 2xx → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (5x2 − 4x − 6)/(3x2 + x + 9).

f(x) = (5x2 − 4x − 6)/(3x2 + x + 9)x → ∞
L =
5.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 =
6.Hard
xyx = 0

Find the limit L = limx→0 (1 − cos 4x)/(3x²), with x in radians.

f(x) = (1 − cos 4x)/(3x²)x → 0
L =

Answer key

  1. 1. L = −32
  2. 2. L = 0.1
  3. 3. L = −2.25
  4. 4. L = 1.667
  5. 5. L = 1.125
  6. 6. L = 2.667

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