Problem 1 - Insert into a sorted array sorting

The program below works similarly to the program we covered in our last class. It takes a value and inserts it into the appropriate place in array A, which in this case is presorted from greatest to least. The rest of the array elements should remain unchanged Use the test value ``7''. Identify the problem and use the Matlab debugger to find and fix the problem.

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  A = [ 50 10 5 2 1 0]; %Initialize Array

x = input('Enter the New Value');

disp('Old Array is ');

disp(A);

current = 1 ; % Initialize array index

  last = size(A,2);  %Get number of elements in array

  % Find the index where x belongs!

while(current<=last)

        if x < A(current)

                current = current + 1;

        else

                break;

        end

end

  % Move all the remaining elements up 1

if (current < last)  % Need to move some up

        for index = last:1:current 

                A(index+1) = A(index);

        end

end

A(current) = x;

disp('New Array is');

disp(A);

Problem 2 - Numerical Integration

The program given below is supposed to implement Simpson's Composite Rule for numerical integration, which states that, given a function f(x), the integral of this function can be approximated by:

  òxNx1f(x)dx @ [(D)/3][f(x1)+4f(x2)+2f(x3)+4f(x4)+2f(x5)¼

  ¼2f(x_N-2)+4f(x_N-1)+f(x_N)

  where D = [((x_N-x₁))/((N-1))] and x_n = x₁+(n-1)D and N is any odd integer (1,3,5,7,9,etc.).

  In this case the program is integrating the function f(x) = x²+4 over the range 0 to 5 with N=9.

Unfortunately, the program is producing the wrong result. Find the bug anf fix the program so that it gives the correct answer for this integral.

File integrate.m:

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    N = 9;  %Number of points in integration

  x1 = 0; % Lower limit of integration

xN = 5; % Upper limit of integration

delta = (xN-x1)/(N-1);

integral = 0;

for n=1:1:N

     xn = x1 + (n-1)*delta;

     if n==1 | n==N

      integral = integral + f(xn);

   elseif mod(n,2)==0

      integral = integral + 4*f(xn);

   else

      integral = integral + 2*f(xn);

   end

   integral = (delta/3)*integral;

end

fprintf('The integral of f.m between %g and %g is %g \n',x1,xN,integral);

  File f.m:

function [y] = f(x)

  y = x^2+4;

Section 2 - Searching and sorting programs.

  For the problems below, use the following array for test data:

A = [1 3 7 5 6 8 2 4 3 7 1 0 9 7 5 8 11 13];

  Problem 3 - Search and Count

Write a Matlab program to determine the frequency with which an element appears in an array, e.g. in the example above, if the element in question was ``7'' your program should report that ``7'' appears three times in the test data. Accept the element to search on as a parameter from the user.

    Problem 4 - Array Sorting

Write a matlab program to implement a ``bubble sort'' to sort the test array above from least to greatest. A bubble sort works according to the following algorithm for an array with N elements:

M=N:

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