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
xy16x = 16

Find the limit L = limx→16 (√x − 4)/(x − 16).

f(x) = (√x − 4)/(x − 16)x → 16
L =
2.Easy
xyx = −1

Find the limit L = limx→−1 (x2 − 4x − 5)/(x + 1).

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

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

f(x) = (4x2 + x − 8)/(4x2 + 5x + 8)x → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (√(9x2 − 2x) − 3x).

f(x) = √(9x2 − 2x) − 3xx → ∞
L =
5.Hard
xyx = 0

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

f(x) = (e−x − 1 + x)/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 = 0.125
  2. 2. L = −6
  3. 3. L = 1
  4. 4. L = −0.3333
  5. 5. L = 0.5
  6. 6. L = 2.667

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