MATLAB: I need help with a taylor series approximation of e^x

approximationfor looptaylor seriestaylor series approximation

Please help!
I have a portion of a code I am trying to write that isn't co-operating. This function is written to approximate e^x by a taylor series expansions using a set number of terms. Earlier on in the code I successfully evaluated the function at 3 and 5 terms. My third task is to figure out how many terms it takes to get an evaluation within 0.000001 error.
%%Necessary Terms %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
errMax = 0.000001;
ex = 1;
nMax = 1000000;
for nInitial=0:nMax
    while abs((exp(x)-ex)/exp(x))*100 >= errMax
        ex = ex + x.^nInitial/factorial(nInitial);
    end
end
fprintf(['The number of terms necessary for the function to be within the allowed error of 0.0001 is ' num2str(nInitial) '.\n']);
fprintf(['The true value of e^3 is ' num2str(exp(3)) '.\n']);
end
Please help!

Best Answer

for nInitial=0:nMax
    if abs((exp(x)-ex)/exp(x))*100 < errMax
      break;
    end
    ex = ex + x.^nInitial/factorial(nInitial);
end
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