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anonymous
 4 years ago
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.
anonymous
 4 years ago
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.

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dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.1i find the ratio to be a constant 3/4

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.1Area 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: \[\frac{a^{3}}{\frac{4a^{3}}{3}} = \frac{3}{4}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Right, thank you very much.
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