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
xy16x = 16

Find the limit L = limx→16 (√x − 4)/(x − 16).

f(x) = (√x − 4)/(x − 16)x → 16
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 + 2x) − x).

f(x) = √(x2 + 2x) − xx → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (1 + 0.5/x)2x. Give a decimal value.

f(x) = (1 + 0.5/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 5x)/(3x²), with x in radians.

f(x) = (1 − cos 5x)/(3x²)x → 0
L =

Answer key

  1. 1. L = 0.125
  2. 2. L = 0.1
  3. 3. L = 1
  4. 4. L = 2.718
  5. 5. L = 3
  6. 6. L = 4.167

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