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
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→∞ (√(x2 + 10x) − x).

f(x) = √(x2 + 10x) − xx → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (x3 − x + 1)/(5x3 + 5x + 2).

f(x) = (x3 − x + 1)/(5x3 + 5x + 2)x → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 ln(1 + 2x)/sin(5x), with x in radians.

f(x) = ln(1 + 2x)/sin(5x)x → 0
L =
6.Hard
xyx = 0

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

f(x) = (e2x − 1 − 2x)/x²x → 0
L =

Answer key

  1. 1. L = 0.125
  2. 2. L = 0.1
  3. 3. L = 5
  4. 4. L = 0.2
  5. 5. L = 0.4
  6. 6. L = 2

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