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 (x3 − 1)/(x − 1).

f(x) = (x3 − 1)/(x − 1)x → 1
L =
2.Easy
xy16x = 16

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

f(x) = (√x − 4)/(x − 16)x → 16
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (1 + 0.5/x)3x. Give a decimal value.

f(x) = (1 + 0.5/x)3xx → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (4x2 + 3x − 1)/(x2 + 6x + 2).

f(x) = (4x2 + 3x − 1)/(x2 + 6x + 2)x → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 ln(1 + x)/sin(4x), with x in radians.

f(x) = ln(1 + x)/sin(4x)x → 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 = 3
  2. 2. L = 0.125
  3. 3. L = 4.482
  4. 4. L = 4
  5. 5. L = 0.25
  6. 6. L = 12.5

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