In this exercise, we work with a discrete problem and show why the relationship is analogous to

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In this exercise, we work with a discrete problem and show why the relationship| Sasmakes sense. Suppose we have a set of equally spaced grid points {a = x0 < x1 < x2 < . . . xn - 1 < xn = b}, where the distance between any two grid points is Δx. Suppose also that at each grid point xk, a function value f(xk) is defined, for k = 0, . . ,n.

a. We now replace the integral with a sum and replace the derivative with a difference quotient. Explain whySåsis
analogous to

b. Simplify the sum in part (a) and show that it is equal to f(b) - f(a).

c. Explain the correspondence between the integral relationship and the summation relationship.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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