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 = 0

Find the limit L = limx→0 (x2 − 6x)/(x).

f(x) = (x2 − 6x)/(x)x → 0
L =
2.Easy
xyx = 2

Find the limit L = limx→2 (x3 − 8)/(x − 2).

f(x) = (x3 − 8)/(x − 2)x → 2
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (√(4x2 + 5x) − 2x).

f(x) = √(4x2 + 5x) − 2xx → ∞
L =
4.Medium
xyy = L

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

f(x) = (1 + 1/x)2xx → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 (e−x − 1 + x)/x².

f(x) = (e−x − 1 + x)/x²x → 0
L =
6.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 =

Answer key

  1. 1. L = −6
  2. 2. L = 12
  3. 3. L = 1.25
  4. 4. L = 7.389
  5. 5. L = 0.5
  6. 6. L = 0.25

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