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
xy1x = 1

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

f(x) = (√x − 1)/(x − 1)x → 1
L =
2.Easy
xy25x = 25

Find the limit L = limx→25 (√x − 5)/(x − 25).

f(x) = (√x − 5)/(x − 25)x → 25
L =
3.Medium
xyy = L

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

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

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

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

Find the limit L = limx→0 (e0.5x − 1 − 0.5x)/x².

f(x) = (e0.5x − 1 − 0.5x)/x²x → 0
L =
6.Hard
xyx = 0

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

f(x) = (1 − cos 5x)/(x²)x → 0
L =

Answer key

  1. 1. L = 0.5
  2. 2. L = 0.1
  3. 3. L = 4.5
  4. 4. L = −1.5
  5. 5. L = 0.125
  6. 6. L = 12.5

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