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
xyx = 1

Find the limit L = limx→1 (x4 − 1)/(x − 1).

f(x) = (x4 − 1)/(x − 1)x → 1
L =
3.Medium
xyy = L

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

f(x) = (−x2 + 1)/(4x2 + 6x + 1)x → ∞
L =
4.Medium
xyy = L

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

f(x) = (1 − 1/x)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 ln(1 + 3x)/sin(2x), with x in radians.

f(x) = ln(1 + 3x)/sin(2x)x → 0
L =

Answer key

  1. 1. L = 0.125
  2. 2. L = 4
  3. 3. L = −0.25
  4. 4. L = 0.3679
  5. 5. L = 2
  6. 6. L = 1.5

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