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Triangle-AOC-inscribed-in-the-region-cut-from-the-parabola-y-x-2-by-the-line-y-a-2-Find-the-limit-of-ratio-of-the-area-of-the-triangle-to-the-area-of-the-parabolic-region-as-a-approaches-zero-




Question Number 144638 by liberty last updated on 27/Jun/21
Triangle AOC inscribed  in the region cut from  the parabola y=x^2  by the  line y=a^2  .Find the limit  of ratio of the area of the  triangle to the area of the  parabolic region as a approaches  zero
TriangleAOCinscribedintheregioncutfromtheparabolay=x2bytheliney=a2.Findthelimitofratiooftheareaofthetriangletotheareaoftheparabolicregionasaapproacheszero
Answered by imjagoll last updated on 27/Jun/21
area △AOC = (1/2).2a.a^2 =a^3   area parabolic=(2/3).2a.a^2 =(4/3)a^3   lim_(a→0)  (a^3 /(((4/3)a^3 ))) = (3/4)
areaAOC=12.2a.a2=a3areaparabolic=23.2a.a2=43a3lima0a3(43a3)=34

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