The while loop for my taylor expansion will not check the condition for each iteration.

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Zachary Nies on 5 Oct 2021

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https://au.mathworks.com/matlabcentral/answers/1467501-the-while-loop-for-my-taylor-expansion-will-not-check-the-condition-for-each-iteration

Answered: Geoff Hayes on 6 Oct 2021

c = pi;
x = (12*pi)/17;
f = x + 1.9 + 0.158*sin(x); %original equation f
f1 = 1 + 0.158*cos(x); %derivative 1
f2 = -0.158*sin(x); %derivative 2
f3 = -0.158*cos(x); %derivative 3
f4 = 0.158*sin(x); %derivative 4
f5 = 0.158*cos(x); %derivative 5  Note: derivative 4 and 5 wll flip for eternity
real_value = c + 1.9 + 0.158*sin(c);
i = 1;
MAXerror = 1;
while MAXerror >= 0.0000001 %while loop will execute until all values stored in variable c is approximated under an error of 0.00001%  
        if i == 1
            
                f_taylor(i) = f; %0th order taylor
                Et(i) = abs(real_value - f_taylor(i))/real_value; 
                
        elseif i == 2
         
                f_taylor(i) = f_taylor(i - 1) + f1.*((c - x).^(i-1)); %1st order taylor
                Et(i) = abs(real_value - f_taylor(i))/real_value;
           
           
        elseif i == 3
           
                f_taylor(i) = f_taylor(i - 1) + (f2/factorial(i-1)).*((c - x).^(i-1)); %2nd order taylor
                Et(i) = abs(real_value - f_taylor(i))/real_value;
         
          
        elseif i == 4
           
                f_taylor(i) = f_taylor(i - 1) + (f3/factorial(i-1)).*((c - x).^(i-1)); %3rd order taylor
                Et(i) = abs(real_value - f_taylor(i))/real_value;
                
  
        elseif i == 5
           
                f_taylor(i) = f_taylor(i - 1) + (f4/factorial(i-1)).*((c - x).^(i-1)); %4th order taylor
                Et(i) = abs(real_value - f_taylor(i))/real_value;
                
           
        elseif mod(i,2) == 0
           
                f_taylor(i) = f_taylor(i - 1) + (f5/factorial(i - 1)).*((c - x).^(i - 1)); %5th order taylor and will cover all odd orders from here on
                Et(i) = abs(real_value - f_taylor(i))/real_value;
        
          
        elseif i > 10000
                fprintf('break')
                break
            
        else
                f_taylor(i) = f_taylor(i - 1) + (f5/factorial(i - 1)).*((c - x).^(i - 1)); %6th order taylor and will cover all even orders from here on
                Et(i) = abs(real_value - f_taylor(i))/real_value;
                
        end
        
 MAXerror = Et(i); %determines the maximum error value in each taylor order
 i = i + 1;
        
end

The loop goes to the maximum i (1000) but should be finished wihin the first 8 loops based on the condition. Debugging found out that the while loop conditon is not checked after the first loop.