P24 - Project 24 MAC 2311 Examine the parabolic arch formed...

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Unformatted text preview: Project 24 MAC 2311 Examine the parabolic arch formed by the function f ( x ) = 3 x- 1 2 x 2 on [ 0 , 6 ] . We would like to approximate its area using rectangles. Sketch the parabola below on [ 0 , 6 ] and shade the area beneath it. Do a quick optimization to find the maximum height of the parabola (instead of using the vertex formula.) At some point you may have seen a formula for such an area as 2 3 BH where H is the height of the arch and B is the width of the base. What is the area of the arch that you shaded above? The Fundamental Theorem of Calculus (Lecture 32) will tell us that this area is given by F (6)- F (0) where F is ANY antiderivative for f . Find an antiderivative for f and show that this process gives the same answer for the area. Now for the approximations (next page). In each case, sketch the half of the parabolic arch on [ 0 , 3 ] and draw the approximating rectangles as instructed. Then evaluate the approxi- mation, KEEPING YOUR WORK WRITTEN AS FRACTIONS. Note that if you have troublemation, KEEPING YOUR WORK WRITTEN AS FRACTIONS....
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P24 - Project 24 MAC 2311 Examine the parabolic arch formed...

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