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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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Question

c. Find a general expression for the right endpoint æ of the kth subinterval [æk-1, æk], where 1 ≤ k ≤ n. Express your answer
in terms of k and n.
Xk =

In this problem you will calculate the area between f(x) = 5x + 9 and the x-axis over the interval [0, 2] using a limit of right-
endpoint Riemann sums:
Area = lim
n→∞
n
(2₁
k=1
f(xk) Ax
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.

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In this problem we will calculate the area between f(x)=9x^2+2 and the x-axis over the interval [0,4] using the limit of right-endpoint Riemann sums shown in the image. 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 [0,4] into n equal width sub intervals [x0, x1], [x1, x2]..., [x n-1, xn] each of width delta-x. Express the width of each subinterval delta-x in terms of the number of subintervals 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. C. Find a general expression for the right endpoint xk of the kth subinterval [x k-1, xk], where 1 is less than or equal to k, which is less than or equal to n. Express your answer in terms of k and n. D. Find f(xk) in terms of k and n. E. Find f(xk)delta-k in terms of k and n. F. Find the value of the…
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