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 = −5

Find the limit L = limx→−5 (x2 + 7x + 10)/(x + 5).

f(x) = (x2 + 7x + 10)/(x + 5)x → −5
L =
2.Easy
xyx = 3

Find the limit L = limx→3 (x2 − x − 6)/(x − 3).

f(x) = (x2 − x − 6)/(x − 3)x → 3
L =
3.Medium
xyy = L

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

f(x) = √(x2 + 3x) − xx → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (√(4x2 − 8x) − 2x).

f(x) = √(4x2 − 8x) − 2xx → ∞
L =
5.Hard
xyx = 0

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

f(x) = (1 − cos 4x)/(4x²)x → 0
L =
6.Hard
xyx = 0

Find the limit L = limx→0 (1 − cos 5x)/(3x²), with x in radians.

f(x) = (1 − cos 5x)/(3x²)x → 0
L =

Answer key

  1. 1. L = −3
  2. 2. L = 5
  3. 3. L = 1.5
  4. 4. L = −2
  5. 5. L = 2
  6. 6. L = 4.167

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