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 = 3

Find the limit L = limx→3 (x3 − 27)/(x − 3).

f(x) = (x3 − 27)/(x − 3)x → 3
L =
2.Easy
xy1x = 1

Find the limit L = limx→1 (√x − 1)/(x − 1).

f(x) = (√x − 1)/(x − 1)x → 1
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (√(9x2 + 7x) − 3x).

f(x) = √(9x2 + 7x) − 3xx → ∞
L =
4.Medium
xyy = L

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

f(x) = √(x2 + 2x) − xx → ∞
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 (e−2x − 1 + 2x)/x².

f(x) = (e−2x − 1 + 2x)/x²x → 0
L =

Answer key

  1. 1. L = 27
  2. 2. L = 0.5
  3. 3. L = 1.167
  4. 4. L = 1
  5. 5. L = 2
  6. 6. L = 2

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