Question

THIS IS USING MATLAB

1. The value of a can be approximated by: a. Write a script which asks the user to input the number of iterations (n), then computes the expression, using a for loop to compute the summation with the specified number of iterations. The larger the number of iterations, the closer the result should be to it. Print out the value of n, and the result using fprintf with 8 digits after the decimal to see the improved precision. b. When your script is working, replace the input statement with a for loop, with a loop index, n, which goes from 1,000 to 10,000 in increments of 1,000. You will now have a loop inside a loop. This outer loop will set n, and your previous code, containing a loop for the summation, will compute pi for that value of n. Don't forget this outer loop's end statement. The result should be a line printed for each computation using a different value of n, something like: n = 1000, approx = 3.14063806 n = 2000, approx = 3.14111527

Answer 1

a) matlab script

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n=input('Enter number of iterations: ');
format long

temp=0;
%for lopp
for k=1:n
temp=temp+(1/k^2);
end

piValue=sqrt(6*temp);

fprintf('Value of pi using %d iterations is %.8f\n',n,piValue);

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Output

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MATLAB R2018a 0 - Search Documentation X Login HOME AFFS PUBISH V EW SGG PLOTS Find File: Compare Print 5 New EDITOR Insert Comment % Indent fx 21. D un Section Advance Run and Open Go To Find - Save Breakpoints Run Run and BREAKPOINTS kamal X Viorkspace Name Value Editor-CAU kama ilindi. pi_findi. mx pi_find. mx + 1 m=input('Enter number of iterations: '); formel long A 1 - E in THAT 107.7075 1000 C Users Current Folder Name anaconda conda config continuum dry clipse idler ipynb_checkpoints python juryter maplollib Mendeley Desktop HH Di FH plValue Ftemp 1000 3.14.15 3.1406 1.6439 temp=0; for lopp for k=1:n Lemp=Lempt (1/x^2); end pivaluc-sqrt (6tomp); [printf("Value of pi using iterations is S. BE\n', 1, pivalue); pylind QWeb Engine Process spyder-py3 tooling 3D Objects E IAnaconda3 anoop ansel Contacts Desktop Details Command Window > > pi findl Enter number of iterations: 100 Value of pi using 100 iterations is 3.13207653 >> pi tindi Enter number of iterations: 1000 Value of ni using 1000 iterations is 3.14063806 fx >> Select a file to view details Type here to search o e le A . ENG 01:56 PM 08-11-2019

format long

%for loop
for n=1000:1000:10000
temp=0;
for k=1:n
temp=temp+(1/k^2);
end
piValue=sqrt(6*temp);
fprintf('n = %d,approx = %.8f\n',n,piValue);
end

============================================================================================

Output

MATLAB R2018a 0 - Search Documentation X Login HOME AFFS PUBISH V EW G G SS PLOTS Find File: Compare Print 5 New EDITOR Insert Comment % Indent fx 21. D un Section Advance Run and Open Go To Find - Save Breakpoint Run - Run and Advance Time BREAKPOINTS kamal OX Workspace Value Editor-C:\Users kamalpi_lindi. pi_find1. m pi_find. mx + 1 en=input('Enter number of iterations: "); formal long Name HAT HE C Users Current Folder Name anaconda conda config continuum dry clipse idler ipynb_checkpoints python juryter maplollib Mendeley Desktop HH Di EpiValue Ftemp 107.7075 10000 10000 3.14.15 3.1415 1.6448 6- 9 - - for loop for n=1000:1000:10000 Lemp=0; for kun temp-temp+ (1/ 2): ond pivalue=sqrt(&*temp); [printf('n = $d, approx = $. end \n', 0, pivalue); pylind QWeb Engine Process spyder-py3 tooling Command Window 3D Objects E IAnaconda3 anoop ansel Contacts Desktop Details > > pi findl n = 1000, apprex = 3.14063806 n - 2000, approx - 3.14111527 n - 3000, approx - 3.14127438 n - 4000, approx - 3.14135394 n = 5000, approx = 3.14140168 n = 6000, approx = 3.14143351 - 7000, apprex - 3.11115624 n - 8000, approx - 3.14147329 n - 9000, approx - 3.14148655 n = 10000, approx = 3.14149716 f4 >> Select a file to view details scnpt Col 27 Ln 9 01:59 PM Type here to search o e la A. 04. ENG 08-11-2019