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In this problem you will calculate the area between f(x) = x² and the x-axis over the interval [3, 10] using a limit of right-endpoint Riemann sums: Area = lim f(xk.) A n4x (˃(²₂)Ax). 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 [3, 10] into n equal width subintervals [0, 1], [1, 2],..., [xn-1, xn] each of width Ax. Express the width of each subinterval Ax in terms of the number of subintervals n. Ax = (10-3)/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 = (Enter a comma separated list.) c. Find a general expression for the right endpoint æ of the kth subinterval [x-1, Xk], where 1 ≤ k ≤ n. Express your answer in terms of k and n. Xk= d. Find f(x) in terms of k and n. f(xk) =

In this problem you will calculate the area between f(x) = x² and the x-axis over the interval [3, 10] using a limit of right-endpoint Riemann sums: Area = lim f(xk.) A n4x (˃(²₂)Ax). 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 [3, 10] into n equal width subintervals [0, 1], [1, 2],..., [xn-1, xn] each of width Ax. Express the width of each subinterval Ax in terms of the number of subintervals n. Ax = (10-3)/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 = (Enter a comma separated list.) c. Find a general expression for the right endpoint æ of the kth subinterval [x-1, Xk], where 1 ≤ k ≤ n. Express your answer in terms of k and n. Xk= d. Find f(x) in terms of k and n. f(xk) =

Algebra & Trigonometry with Analytic Geometry
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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In this problem you will calculate the area between f(x) = x² and the x-axis over the interval [3, 10] using a limit of right-endpoint Riemann sums: Ax= Area: = = 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 [3, 10] into n equal width subintervals [X0, X1], [X1, X2], . n-1, xn] each of width Ax. Express the width of each subinterval Ax in terms of the number of subintervals n. (10-3)/n n lim (Σf(xk)Δα k=1 = b. Find the right endpoints x1, x2, 3 of the first, second, and third subintervals [x0, x1], [x1, x2], [x2, x3] and express your answers in terms of n. X1, X2, X3 = (Enter a comma separated list.) d. Find f(x) in terms of k and n. f(xk) = c. Find a general expression for the right endpoint x of the kth subinterval [*k-1, Xk], where 1 ≤ k ≤ n. Express your answer in terms of k and n. Xk=
Transcribed Image Text:In this problem you will calculate the area between f(x) = x² and the x-axis over the interval [3, 10] using a limit of right-endpoint Riemann sums: Ax= Area: = = 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 [3, 10] into n equal width subintervals [X0, X1], [X1, X2], . n-1, xn] each of width Ax. Express the width of each subinterval Ax in terms of the number of subintervals n. (10-3)/n n lim (Σf(xk)Δα k=1 = b. Find the right endpoints x1, x2, 3 of the first, second, and third subintervals [x0, x1], [x1, x2], [x2, x3] and express your answers in terms of n. X1, X2, X3 = (Enter a comma separated list.) d. Find f(x) in terms of k and n. f(xk) = c. Find a general expression for the right endpoint x of the kth subinterval [*k-1, Xk], where 1 ≤ k ≤ n. Express your answer in terms of k and n. Xk=
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