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In this problem you will calculate the area between f(x) = x² and the x-axis over the interval [2,9] using a limit of right-endpoint Riemann sums: Express the following quantities in terms of n, the number of rectangles in the Riemann sum, and k, the index for the rectangles in the Riemann sum. [xn-1, Xn] a. We start by subdividing [2, 9] into n equal width subintervals [x0, x₁ ], [x₁, x₂], . each of width Ax. Express the width of each subinterval Ax in terms of the number of subintervals n. Ax = 7/n b. Find the right endpoints X₁, X2, X3 of the first, second, and third subintervals [x0, x1 ], [x₁, x₂], [x2, x3] and express your answers in terms of n. X1, X2, X3 = 2+7/n, 2+14/n, 2+21/n c. Find a general expression for the right endpoint x of the kth subinterval [xk-1, xk], where 1 ≤ k ≤n. Express your answer in terms of k and n. Xk = 2+7k/n d. Find f(x) in terms of k and n. f(x) = (2+7k/n)^2 n Area = lim (7,34x) (x^x). n→∞ k=1 e. Find f(x)Ax in terms of k and n. f(xk)Ax = (2+7k/n)^2(7/n) k=1 f. Find the value of the right-endpoint Riemann sum in terms of n. n Σf(x)Ax= lim n→∞ g. Find the limit of the right-endpoint Riemann sum. - ( = n = Σf(xk) Ax k=1 (Enter a comma separated list.)

In this problem you will calculate the area between f(x) = x² and the x-axis over the interval [2,9] using a limit of right-endpoint Riemann sums: Express the following quantities in terms of n, the number of rectangles in the Riemann sum, and k, the index for the rectangles in the Riemann sum. [xn-1, Xn] a. We start by subdividing [2, 9] into n equal width subintervals [x0, x₁ ], [x₁, x₂], . each of width Ax. Express the width of each subinterval Ax in terms of the number of subintervals n. Ax = 7/n b. Find the right endpoints X₁, X2, X3 of the first, second, and third subintervals [x0, x1 ], [x₁, x₂], [x2, x3] and express your answers in terms of n. X1, X2, X3 = 2+7/n, 2+14/n, 2+21/n c. Find a general expression for the right endpoint x of the kth subinterval [xk-1, xk], where 1 ≤ k ≤n. Express your answer in terms of k and n. Xk = 2+7k/n d. Find f(x) in terms of k and n. f(x) = (2+7k/n)^2 n Area = lim (7,34x) (x^x). n→∞ k=1 e. Find f(x)Ax in terms of k and n. f(xk)Ax = (2+7k/n)^2(7/n) k=1 f. Find the value of the right-endpoint Riemann sum in terms of n. n Σf(x)Ax= lim n→∞ g. Find the limit of the right-endpoint Riemann sum. - ( = n = Σf(xk) Ax k=1 (Enter a comma separated list.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.6: Permutations
Problem 47E
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In this problem you will calculate the area between f(x) = x² and the x-axis over the interval [2,9] using a limit of right-endpoint Riemann sums: n Area = lim Σf() Δx k=1 Express the following quantities in terms of n, the number of rectangles in the Riemann sum, and k, the index for the rectangles in the Riemann sum. a. We start by subdividing [2, 9] into n equal width subintervals [xo, x1], [x1, x2], ... , [Xp-1, Xn] each of width Ax. Express the width of each subinterval Ax in terms of the number of subintervalsn. Ax = 7/n b. Find the right endpoints x1, x2, X3 of the first, second, and third subintervals [X0, x1 ], [x1, x2], [x2, x3] and express your answers in terms of n. X1, X2, X3 = 2+7/n, 2+14/n, 2+21/n (Enter a comma separated list.) c. Find a general expression for the right endpoint xỵ of the kth subinterval [xx-1, Xg], where 1 <k< n. Express your answer in terms of k and n. X = 2+7k/n d. Find f(xx) in terms of k and n. f(xx) = (2+7k/n)^2 e. Find f(xx)Ax in terms of k and n. f(x)Ax = (2+7k/n)^2(7/n) f. Find the value of the right-endpoint Riemann sum in terms of n. п Ef(x)Ax = %D k=1 g. Find the limit of the right-endpoint Riemann sum. n lim Ef(xx)Ax k=1
Transcribed Image Text:In this problem you will calculate the area between f(x) = x² and the x-axis over the interval [2,9] using a limit of right-endpoint Riemann sums: n Area = lim Σf() Δx k=1 Express the following quantities in terms of n, the number of rectangles in the Riemann sum, and k, the index for the rectangles in the Riemann sum. a. We start by subdividing [2, 9] into n equal width subintervals [xo, x1], [x1, x2], ... , [Xp-1, Xn] each of width Ax. Express the width of each subinterval Ax in terms of the number of subintervalsn. Ax = 7/n b. Find the right endpoints x1, x2, X3 of the first, second, and third subintervals [X0, x1 ], [x1, x2], [x2, x3] and express your answers in terms of n. X1, X2, X3 = 2+7/n, 2+14/n, 2+21/n (Enter a comma separated list.) c. Find a general expression for the right endpoint xỵ of the kth subinterval [xx-1, Xg], where 1 <k< n. Express your answer in terms of k and n. X = 2+7k/n d. Find f(xx) in terms of k and n. f(xx) = (2+7k/n)^2 e. Find f(xx)Ax in terms of k and n. f(x)Ax = (2+7k/n)^2(7/n) f. Find the value of the right-endpoint Riemann sum in terms of n. п Ef(x)Ax = %D k=1 g. Find the limit of the right-endpoint Riemann sum. n lim Ef(xx)Ax k=1
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