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Problem 4: Understanding of discretization of variables and iterations (using an example of a series summation) Write a function (numerical solver) to evaluate the sum of the squared of a continuous function f(x(k), k = 1,2,3, evaluated at the discretized vector array x ranging from a to b (meaning that x = 11 n space (a, b, k), so that the sum does not exceed maxsum. Also determine the maximum number of terms required in the summation, which cannot exceed maxitr. Test on the example of f ()x, a1, b- 3, maxsum 1000, and maxtr = 20 Study the sequence of examples discussed in Lecture 03 notes.] Example Consider f (x) = x, a = 1, b= 3, ma x sum = 10. Forn-3, the sum is 12 +22+32=14 which exceeds the maximum allowable sum of 10. For n=2, the sum is 12 +32 = 10 which does not exceed the maxsum of 10. Hence n-2 is the maximum number of terms in the discretization of the x-variable such that the sum satisfies: ((x())s maxsum The mathematical problem is to determine the number of terms in the discretization of the variable x and the summation such that f(x(k)))s maxsum. Note that as n increases, so does the number of elements of x. This is a fundamental concept in digitization, e.g., in digital control problems. Consider the example: f ( x) = x, a 1, b= 3, ma x sum = 10, For n=3, the sum is 12 +22 +32 14 which exceeds the maximum allowable sum of 10 For n=2 the sum is 12 +32-10 which does not exceed the max sum of 10, Hence n=21s the maximum number of terms in the diseretization of the x-variable such that (f(x(k) s maxsum Note: First study the sequence of problems posted on the lecture journal #3 (listed as Problem I, Problem 2, etc.). This problem is the "Problem 4