anonymous
  • anonymous
The figure here shows triangle AOC inscribed in the region cut from the parabola y=x^2 by the line y=a^2. Find the limit of the ratio of the area of the triangle to the area of the parabolic region as a approaches zero.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
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dumbcow
  • dumbcow
i find the ratio to be a constant 3/4
dumbcow
  • dumbcow
Area of triangle = (1/2)*2a*a^2 = a^3 Area of parabolic region = \[2\int\limits_{0}^{a}(a^{2}-x^{2}) dx = \frac{4a^{3}}{3}\] Ratio: \[\frac{a^{3}}{\frac{4a^{3}}{3}} = \frac{3}{4}\]

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anonymous
  • anonymous
Right, thank you very much.
dumbcow
  • dumbcow
your welcome

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