Скачать или смотреть Estimating Area Under the Curve using Left/Right Endpoint Reimann Sums

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Question: Estimate the area under the graph of
(A) Estimate the area under the graph of f(x)=16-x2, from x=0 to x=4 using 4 approximating rectangles and right endpoints estimateleft endpoints estimate: Right endpoints estimate

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Answered By:

Johnny M.
Mathematics Ph. D. Student
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Written Explanation:

Begin by drawing the graphs and rectangles for the left/right endpoint estimations to assist with visualizing the area.Left Endpoint Estimation:L = (1)(16) + (1)(15) + (1)(12) + (1)(7)L = 50 (Overestimation)Right Endpoint Estimation:R = (1)(0) + (1)(7) + (1)(12) + (1)(15)R = 34 (Underestimation)ANSWERS: L = 50 and R = 34
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