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
xy25x = 25

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

f(x) = (√x − 5)/(x − 25)x → 25
L =
2.Easy
xyx = −4

Find the limit L = limx→−4 (x2 + 9x + 20)/(x + 4).

f(x) = (x2 + 9x + 20)/(x + 4)x → −4
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (1 + 2/x)3x. Give a decimal value.

f(x) = (1 + 2/x)3xx → ∞
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(2x), with x in radians.

f(x) = ln(1 + x)/sin(2x)x → 0
L =
6.Hard
xyx = 0

Find the limit L = limx→0 (e0.5x − 1 − 0.5x)/x².

f(x) = (e0.5x − 1 − 0.5x)/x²x → 0
L =

Answer key

  1. 1. L = 0.1
  2. 2. L = 1
  3. 3. L = 403.4
  4. 4. L = 1
  5. 5. L = 0.5
  6. 6. L = 0.125

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