Solved: Graphical Reasoning Consider the region bounded by the graphs of and as shown in

Chapter 5, Problem 77

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Graphical Reasoning Consider the region bounded by the graphs of and as shown in the figure. To print an enlarged copy of the graph, go to the website www.mathgraphs.com. (a) Redraw the figure, and complete and shade the rectangles representing the lower sum when Find this lower sum. (b) Redraw the figure, and complete and shade the rectangles representing the upper sum when Find this upper sum. (c) Redraw the figure, and complete and shade the rectangles whose heights are determined by the functional values at the midpoint of each subinterval when Find this sum using the Midpoint Rule. (d) Verify the following formulas for approximating the area of the region using subintervals of equal width. Lower sum: Upper sum: Midpoint Rule: (e) Use a graphing utility and the formulas in part (d) to complete the table. (f) Explain why increases and decreases forincreasing values of as shown in the table in part (e).

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