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Verizon 11:32 math hone.pdf Calculus AB Assignment Finding a Better Approximation of Area Under a Curve You'll be working with the function y =f(x) (x 1.5) + + 2, and the interval you'll always be concerned about is [2, 6]. Here's a graph. 4 3.5 3 2.5 2 1.5 0.5 -2 2 3 x 4 5 6 You'll need to have the graph (above) on paper, so you'll need to print it or draw it on paper. You'll need at least three copies. I'll call them your "paper graphs." The actual area under the curve on the interval [2, 6] is about 17.586. Approximating the area under the curve on the interval [2, 6] by using a Riemann sum with 4 equal subdivisions and left-hand endpoints gives you 14.976. Draw the rectangles used for this Riemann sum on one of your paper graphs. Do you see where the error for this approximation is? Approximating the area under the curve on the interval [2, 6] by using a Riemann sum with 4 equal subdivisions and right-hand endpoints gives you R 2(/(0) -Ff(2) +f(4) +f(6)) = 21.314. Draw the rectangles used for this Riemann sum on one of your paper graphs. Do you see where the error for this approximation is? Now, you'll try to improve these approximations. (Remember, the interval you're always working with is [2, 6].) 1. Re-compute the Riemann sum, but this time increase the number of subdivisions. Take n to be at least 8 (with equal subdivisions) and compute a Riemann sum using either left-hand endpoints or right-hand endpoints. Show all your computation work and compare the approximation to the Riemann sum using only 4 subdivisions and the same endpoint scheme. (Note: You don't need to show function evaluations, so it's okay to write, for example,f(12) + (13) +f(14) [answer], and let your calculator compute the answer, as long as it's correct.) 1 Copyright 0 2021 Apex Learning. See Terms of Use for further information. Images of the T 1-84 calculator are used with the permission of Texas Instruments Incorporated. Copyright 0 2011 Texas Instruments Incorporated. Calculus AB Assignment Finding a Better Approximation of Area Under a Curve