Question

THE CODE NEEDS TO BE ON MATLAB

2. Exercise (a) Let's write a script file that calculates exp(2) by a Maclaurin series using a while loop exp x )=-+-+-+-+ The while loop should add each of the series terms. The program error as defined below is smaller than 0.01. Error is the exact value (i.e. exp(2)), minus the approximate value (i.e., the current series sum) should exit the loop when the absolute absolute error-lexact-approx Use fprintf within the loop such that, during each round of iteration, the number of iteration, current approximation (i.e. sum of series), and the absolute error are displayed. Also, report exact value once at the end of the program using fprintf. You can use built-in functions like factorial) and abs() The displayed result may look like the following lab8 4 iter- approx- 1.000, error 6.389 ter= 2, . (more lines like the above) exact value- (b) If you integrate cos(t) from t-0 to t-b, for what value of b does the integral become 0.5? You can refer to the program on the previous page. Use a while loop to stop iteration when the integral is 0.5 or above. Generate a text output on screen that reports the upper limit b and the integral.

Answer 1

error=1; %starting value for error

maclaurin_value=0; % starting value for value calculated from maclaurin series

n=0; %starting power

x=2; %power to which e has to be raised to

i=0; %iteration number

while error > 0.01

      i=i+1; %increment iteration number

     maclaurin_value=maclaurin_value+ (x^n)/factorial(n);   %calculate approximation

     error=abs(exp(2)-maclaurin_value); %calculate error

     fprintf("iter = %d",i);

     fprintf(", approx = %f",maclaurin_value);

     fprintf(", error = %f \n",error);

     n=n+1;    %increment exponent to get the next term in the maclaurin series

end

fprintf("exact value = %f",exp(2));

Output of this script

2. The second question refers to a program which is not included in the question. Please include the program which is (according to the question) available on the previous page.