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Letf(x)=4x. (a) Sketch the region R under the graph of fon the interval (0, 2). y 1 2 3 Find its exact area using geometry. square units 5 6 DOO 1 (c) Repeat part (b) with eight subintervals of equal length (n=8). square units 2 3 3 6 4 2 1 2 3 (b) Use a Riemann sum with four subintervals of equal length (n=4) to approximate the area of R. Choose the representative points to be the left endpoints of the subintervals. square units (d) Compare the approximations obtained in parts (b) and (c) with the exact area found in part (a). Do the approximations improve with larger in? O Yes O No 5 7 4 2 1 2 3 6

Letf(x)=4x. (a) Sketch the region R under the graph of fon the interval (0, 2). y 1 2 3 Find its exact area using geometry. square units 5 6 DOO 1 (c) Repeat part (b) with eight subintervals of equal length (n=8). square units 2 3 3 6 4 2 1 2 3 (b) Use a Riemann sum with four subintervals of equal length (n=4) to approximate the area of R. Choose the representative points to be the left endpoints of the subintervals. square units (d) Compare the approximations obtained in parts (b) and (c) with the exact area found in part (a). Do the approximations improve with larger in? O Yes O No 5 7 4 2 1 2 3 6

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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6.3 Q1

Letf(x)=4x. (a) Sketch the region R under the graph of fon the interval (0, 2). y 1 2 3 Find its exact area using geometry. square units 5 6 DOO 1 (c) Repeat part (b) with eight subintervals of equal length (n=8). square units 2 3 3 6 4 2 1 2 3 (b) Use a Riemann sum with four subintervals of equal length (n=4) to approximate the area of R. Choose the representative points to be the left endpoints of the subintervals. square units (d) Compare the approximations obtained in parts (b) and (c) with the exact area found in part (a). Do the approximations improve with larger in? O Yes O No 5 7 4 2 1 2 3 6
Transcribed Image Text:Letf(x)=4x. (a) Sketch the region R under the graph of fon the interval (0, 2). y 1 2 3 Find its exact area using geometry. square units 5 6 DOO 1 (c) Repeat part (b) with eight subintervals of equal length (n=8). square units 2 3 3 6 4 2 1 2 3 (b) Use a Riemann sum with four subintervals of equal length (n=4) to approximate the area of R. Choose the representative points to be the left endpoints of the subintervals. square units (d) Compare the approximations obtained in parts (b) and (c) with the exact area found in part (a). Do the approximations improve with larger in? O Yes O No 5 7 4 2 1 2 3 6
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