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 (x2 − 2x − 3)/(x + 1).

f(x) = (x2 − 2x − 3)/(x + 1)x → −1
L =
2.Easy
xyx = 2

Find the limit L = limx→2 (x4 − 16)/(x − 2).

f(x) = (x4 − 16)/(x − 2)x → 2
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (−2x2 + 4x − 1)/(5x2 + 3x + 9).

f(x) = (−2x2 + 4x − 1)/(5x2 + 3x + 9)x → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (1 + 2/x)2x. Give a decimal value.

f(x) = (1 + 2/x)2xx → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 ln(1 + 3x)/sin(x), with x in radians.

f(x) = ln(1 + 3x)/sin(x)x → 0
L =
6.Hard
xyx = 0

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

f(x) = (1 − cos 3x)/(4x²)x → 0
L =

Answer key

  1. 1. L = −4
  2. 2. L = 32
  3. 3. L = −0.4
  4. 4. L = 54.6
  5. 5. L = 3
  6. 6. L = 1.125

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