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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.

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  1. anonymous
    • 4 years ago
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  2. dumbcow
    • 4 years ago
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    i find the ratio to be a constant 3/4

  3. dumbcow
    • 4 years ago
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    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: \[\frac{a^{3}}{\frac{4a^{3}}{3}} = \frac{3}{4}\]

  4. anonymous
    • 4 years ago
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    Right, thank you very much.

  5. dumbcow
    • 4 years ago
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    your welcome

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