An IMC student wants to determine an approximation of the square root of 2 and uses continued fractions for it. It is 1 √√2 1+ 1 2+ 2+ 1 2+... Which of the following MATLAB codes cannot be used in order to compute a correct approximation? Code A function [] continued_fraction() % using a for-loop x=2; for k=1:10 x=2+1/(2+1/x); end result=x-1 end Code B function [x] = continued_fraction(n,x) % using a recurrence relation % start for example with: % continued_fraction (10,2) if n>=1 x = continued fraction (n-1,2+1/(2+1/x)); else x=x-1; end end Code C function []=continued_fraction() % using a while-loop and an % anonymous function myfun=@(x) 2+1/(2+1/x); deviation=1; x=2; while abs(deviation)>1e-06 x_new myfun(x); deviation=x_new-x; x=x_new; end result=x-1 end Code D function []=continued_fraction() % using vectors and a separate function x=2; n=10; vec=ones(n,1).*x; vec(2:end)=vec(1:end-1)+... 1./calc frac/vec(1:end-1)); res=max(vec)-1 end function [x_out]=calc_frac{x_in) x_out 2+1./(2+1./x_in); end
An IMC student wants to determine an approximation of the square root of 2 and uses continued fractions for it. It is 1 √√2 1+ 1 2+ 2+ 1 2+... Which of the following MATLAB codes cannot be used in order to compute a correct approximation? Code A function [] continued_fraction() % using a for-loop x=2; for k=1:10 x=2+1/(2+1/x); end result=x-1 end Code B function [x] = continued_fraction(n,x) % using a recurrence relation % start for example with: % continued_fraction (10,2) if n>=1 x = continued fraction (n-1,2+1/(2+1/x)); else x=x-1; end end Code C function []=continued_fraction() % using a while-loop and an % anonymous function myfun=@(x) 2+1/(2+1/x); deviation=1; x=2; while abs(deviation)>1e-06 x_new myfun(x); deviation=x_new-x; x=x_new; end result=x-1 end Code D function []=continued_fraction() % using vectors and a separate function x=2; n=10; vec=ones(n,1).*x; vec(2:end)=vec(1:end-1)+... 1./calc frac/vec(1:end-1)); res=max(vec)-1 end function [x_out]=calc_frac{x_in) x_out 2+1./(2+1./x_in); end
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.3: Quadratic Equations
Problem 81E
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