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 − 7x + 6)/(x − 1).

f(x) = (x2 − 7x + 6)/(x − 1)x → 1
L =
2.Easy
xyx = 2

Find the limit L = limx→2 (x2 − 7x + 10)/(x − 2).

f(x) = (x2 − 7x + 10)/(x − 2)x → 2
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (√(x2 − 5x) − x).

f(x) = √(x2 − 5x) − xx → ∞
L =
4.Medium
xyy = L

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

f(x) = (x2 + 2x + 4)/(4x2 + 5x + 1)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 (1 − cos 3x)/(x²), with x in radians.

f(x) = (1 − cos 3x)/(x²)x → 0
L =

Answer key

  1. 1. L = −5
  2. 2. L = −3
  3. 3. L = −2.5
  4. 4. L = 0.25
  5. 5. L = 2
  6. 6. L = 4.5

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