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
xy9x = 9

Find the limit L = limx→9 (√x − 3)/(x − 9).

f(x) = (√x − 3)/(x − 9)x → 9
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→∞ (2x2 − 2x − 7)/(5x2 + 2x + 8).

f(x) = (2x2 − 2x − 7)/(5x2 + 2x + 8)x → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (1 + 0.5/x)2x. Give a decimal value.

f(x) = (1 + 0.5/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 (e−0.5x − 1 + 0.5x)/x².

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

Answer key

  1. 1. L = 0.1667
  2. 2. L = 0.1
  3. 3. L = 0.4
  4. 4. L = 2.718
  5. 5. L = 0.5
  6. 6. L = 0.125

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