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 = 4

Find the limit L = limx→4 (x2 − 16)/(x − 4).

f(x) = (x2 − 16)/(x − 4)x → 4
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→∞ (√(4x2 + 9x) − 2x).

f(x) = √(4x2 + 9x) − 2xx → ∞
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 5x)/(2x²), with x in radians.

f(x) = (1 − cos 5x)/(2x²)x → 0
L =
6.Hard
xyx = 0

Find the limit L = limx→0 ln(1 + 4x)/sin(2x), with x in radians.

f(x) = ln(1 + 4x)/sin(2x)x → 0
L =

Answer key

  1. 1. L = 8
  2. 2. L = 0.5
  3. 3. L = 2.25
  4. 4. L = 0.3679
  5. 5. L = 6.25
  6. 6. L = 2

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