(g) Now, redo the rectangle approximation with 8 rectangles (that is, calculate Rs). How close is Rs to the actual area? (h) Geogebra has an online tool for calculating Riemann sums. Go to www.geogebra.org/m/h4P4cjsT (type it carefully). To use it, you enter a function, an interval [a, b], and a number of rect- angles n, so enter x² in the function field, a = 0 and b = 1. Then change the checkbox from Left Riemann Sum to Right Riemann sum. In the field for n, enter 25, 50, and 100 and record the values for R25, R50, and R100. Are these closer to the actual area of 1/3 than the values you got for R4 and Rg? 81x (i) If Rn is the approximation using n rectangles, what do you think the exact value of lim Rn? Or, put another way, what do you think would happen if we could calculate the approxi- mation with infinitely many rectangles?
(g) Now, redo the rectangle approximation with 8 rectangles (that is, calculate Rs). How close is Rs to the actual area? (h) Geogebra has an online tool for calculating Riemann sums. Go to www.geogebra.org/m/h4P4cjsT (type it carefully). To use it, you enter a function, an interval [a, b], and a number of rect- angles n, so enter x² in the function field, a = 0 and b = 1. Then change the checkbox from Left Riemann Sum to Right Riemann sum. In the field for n, enter 25, 50, and 100 and record the values for R25, R50, and R100. Are these closer to the actual area of 1/3 than the values you got for R4 and Rg? 81x (i) If Rn is the approximation using n rectangles, what do you think the exact value of lim Rn? Or, put another way, what do you think would happen if we could calculate the approxi- mation with infinitely many rectangles?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 68E
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