Question

4. One interesting property of a Fibonacci sequence is that the ratio of the values of adjacent members of the sequence approaches a number called "the golden ratio". Create a program that accepts the first two numbers of a Fibonacci sequence as user input and then calculates additional values in the sequence until the ratio of adjacent values converges to within 0.001 You can do this in a while loop by comparing the ratio of element k to element k - 1 and the ratio of element k - 1 to element k - 2. If you call your sequence r, then the code for the while statement i while abs(x(k)/x(k -1)-r(k - 1)/x(k -2)) 0.001 5. Edmond Halley (the astronomer famous for discovering Halley's comet) invented a fast algorithm for computing the square root of a number, A. Halley's algorithm approximates A as follows: Start with an initial guess x1. The new approximation is then given by 2 (15 yn (10 - 3yn) These two calculations are repeated until some convergence criterion, E, is met. Write an m-file that approximates the square root of a number. It should prompt the user to enter two inputs, the initial guess and the convergence criterion. Test your code by comparing it to the value calculated with the built-in MATLAB function, sqrt

Answer 1

Please find the code below::::

1)

clc
clear
num1 = input('Please enter first sequence : ');
num2 = input('Please enter second sequence : ');
tmp1 = num1+num2;
ratio = 0;
fprintf('Sequences are as below\n');
while true
diff1 = tmp1/num2;
diff2 = num2/num1;
ratio = abs(diff1 - diff2);
fprintf("Next Sequence : %d Ratio : %.3f\n",tmp1,ratio);
if ratio<=0.001
break;
end
num1 = num2;
num2 = tmp1;
tmp1 = num1+num2;
  
end

2)

clc

clear

a = input('number ');

x = input('guess ');

tol = 0.000001;

dif=inf;

while dif>=tol

y=(1/a)*x^2;

n = ((x/8)*(15-y*(10-3*y)));

dif= (abs(n-x));

disp(n)

x=n;

end

disp(n)

BREAKPOINTS RUN anguage_workspace matlab staticClass2 Editor - C:Users Mohammad Shahrukh\Desktop\c language_workspace\ matlablstatic harrleysComitGetSquareRoot.mx+ -clc -clear a input ('Please enter number x =11 %start with guess I tol-0.000001; -dif-inf; while dif>-tol n-((x/8) (15-y* (10-3*y))) dif= (abs (n-x) ) ; X-n: end fprint f ("Square root of %d is %.2f\n", a,n);

output:

ablstaticClass2 harrleys Command Window Please enter number 400 Square root of 400 is 20.00