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 = 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 + 4x) − 2x).

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

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

f(x) = √(4x2 − 4x) − 2xx → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 ln(1 + x)/sin(5x), with x in radians.

f(x) = ln(1 + x)/sin(5x)x → 0
L =
6.Hard
xyx = 0

Find the limit L = limx→0 ln(1 + 3x)/sin(5x), with x in radians.

f(x) = ln(1 + 3x)/sin(5x)x → 0
L =

Answer key

  1. 1. L = 0.125
  2. 2. L = 12
  3. 3. L = 1
  4. 4. L = −1
  5. 5. L = 0.2
  6. 6. L = 0.6

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