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 = 2

Find the limit L = limx→2 (x4 − 16)/(x − 2).

f(x) = (x4 − 16)/(x − 2)x → 2
L =
2.Easy
xy25x = 25

Find the limit L = limx→25 (√x − 5)/(x − 25).

f(x) = (√x − 5)/(x − 25)x → 25
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (√(9x2 − 4x) − 3x).

f(x) = √(9x2 − 4x) − 3xx → ∞
L =
4.Medium
xyy = L

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

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

Find the limit L = limx→0 (e2x − 1 − 2x)/x².

f(x) = (e2x − 1 − 2x)/x²x → 0
L =
6.Hard
xyx = 0

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

f(x) = (1 − cos 4x)/(x²)x → 0
L =

Answer key

  1. 1. L = 32
  2. 2. L = 0.1
  3. 3. L = −0.6667
  4. 4. L = 0.1353
  5. 5. L = 2
  6. 6. L = 8

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