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

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!

Answer 1

[Walter Roberson]

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

[Thomas MacDowell]

that worked, but it seems like the amount of terms I need to have to be within the acceptable error (0.000001) is way to high for matlab to handle, unless I am missing something else.

[Walter Roberson]

You are multiplying the relative difference by 100, so you are checking not for an error of 0.000001 but rather an error of 0.000001 percent -- so a relative error of 0.00000001

[Thomas MacDowell]

at the 647th term in the series it turns into 'NaN' which is why it isn't giving me an answer, how can I get the number of terms? I'mm pulling my hair out over this

[Walter Roberson]

Your calculation is off by 1.0. Initialize ex to 0 instead of 1.

Answer 2

[sparsh mehta]

or nInitial=0:nMax

if abs((exp(x)-ex)/exp(x))*100 < errMax

break;

end

ex = ex + x.^nInitial/factorial(nInitial);

end