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 = −4

Find the limit L = limx→−4 (x2 + 6x + 8)/(x + 4).

f(x) = (x2 + 6x + 8)/(x + 4)x → −4
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (√(4x2 − 3x) − 2x).

f(x) = √(4x2 − 3x) − 2xx → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (√(x2 + 7x) − x).

f(x) = √(x2 + 7x) − xx → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 (1 − cos 3x)/(4x²), with x in radians.

f(x) = (1 − cos 3x)/(4x²)x → 0
L =
6.Hard
xyx = 0

Find the limit L = limx→0 (e−0.5x − 1 + 0.5x)/x².

f(x) = (e−0.5x − 1 + 0.5x)/x²x → 0
L =

Answer key

  1. 1. L = 0.125
  2. 2. L = −2
  3. 3. L = −0.75
  4. 4. L = 3.5
  5. 5. L = 1.125
  6. 6. L = 0.125

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