Question

part 2 to the problem in matlabthis is the hint that came with the problem

The value of T can be estimated from the following equation: In your script file, estimate the value of t for any number of terms. You must ask the user for the desired number of terms and calculate the absolute error/difference between your calculation and the built-in MATLAB value ofpi. Display your results with the following message (including the asterisks) where II is the number of terms used to calculate π, F . FFFFFFFFFF is your final result printed out with %f with 10 digits past the decimal point, and E. EEEEEEEE is the absolute error/difference between your calculation and pi printed out with %E with 8 digits past the decimal point. For 11 terms the estimated value of P1 = F. FFFFFFFFFF with an absolute difference of E.EEEEEEEE with pi in MATLAEB You may test your program with 5, 10, and 40 terms. HINT: Use a for loop to calculate the product above. Note that the numerator of term 1 is V2+0 and numerator of term 2 is /2 + numerator of term 1. This pattern is repeated for the rest of terms. Also, note that every numerator is divided by 2. The final value of pi can then be calculated from the completed product. It is strongly recommended that you use the in-class activities and lecture notes as a model for how to write your code. HINTS: Start by prompting the user to enter in a value for x and a tolerance (enforce that the tolerance is a correct value). Then, write your while loop to estimate f(x) using the infinite series for a single x value, i.e. if x was a scalar, and the provided tolerance. Modify your while loop conditional to account for a maximum number of iterations. Test your code with x = -2 and a tolerance of IE-1, 1E-5, 1E-10. Check your answers with the value of (1x) exp (x) in MATLAB. Modify your code to estimate f(x) if x is a vector. This can be done by putting a for loop around your calculation for x as a scalar and iterating through each value of x in the vector one at a time to calculate the appropriate f(x) value. Test your code with x --3:3 and a tolerance of 1E-8. Check your answers with the value of (1 x) .* exp (x) in MATLAB. Modify your code one more time to estimate f(x) if x is a matrix. This can be done by adding one more for loop around your calculatation for x as a vector to iterate through each (row, column) element of your matrix to calculate the appropriate f(x) value. Test your code with x = [ 1 : 4 ; -4:-1 ; 7 : 10 ] and a tolerance of 1E-8. Check your answers with the value of (1+x) * exp (x) in MATLAB.

Answer 1

n=input('enter the number of terms\n');
trueval=pi;
num(1)=sqrt(2);
deno=2;
x=num(1)/deno;
for i=2:n
num(i)=sqrt(2+num(i-1));
newx=x*num(i)/deno;
x=newx;
end
EPI=(1/x)*2;
err=abs(trueval-EPI);
fprintf('For %d terms the estimated value of PI=%.10f with an\n absolute error difference of %.8f with pi in MATLAB',n,EPI,err)

Command Window >noia enter the number of terms For 5 terms the estimated value of PI-3.1403311570 with an absolute error difference of 0.00126150 with pi in MATLAB>> >>noia enter the number of terms 10 For 10 terms the estimated value of PI-3.1415914215 with an absolute error difference of 0.00000123 with pi in MATLAB>> >>noia enter the number of terms For 40 terms the estimated value of PI-3.1415926536 with an J absolute error difference of 0.00000000 with pi in MATLAB>>