In this exercise, we work with a discrete problem and show why the relationship is analogous to b. Simplify the sum in part (a) and

In this exercise, we work with a discrete problem and show why the relationshipmakes sense. Suppose we have a set of equally spaced grid points {a = x₀ 1 2 n - 1 n = b}, where the distance between any two grid points is Δx. Suppose also that at each grid point xk, a function value f(x_k) is defined, for k = 0, . . ,n.

a. We now replace the integral with a sum and replace the derivative with a difference quotient. Explain whyis
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.

| Sas"(x) dx = f(b) f(a) Ss"(x) dx a.