Reference no: EM13168343

writing a matlab script to approximate exp(x) at exp(.05) using ""Taylor series"" ""and"" a ""while loop"".

a=.05 is very close to a convenient x value. The allowable error (error = |guess-true|) is to be less than or equal to 10^-9.

I also need to figure out how many terms in the Taylor series were required to achieve convergence. Plot the n=1, n=2, n=3 approximations to e^x for x=0:0.05:1, and plot the built-in exp(x) function on this same interval. Ensure that each line has a unique LineSpec format (ie- line style, tickmark, color), and provide a legend identifying your four curves. Label x and y axes as "Domain" and "Range".

 

This is what I have so far. How do I add the 3 n values. I JUST NEED TO ADD THE N-1, N-2, N-3 But I don't know how.

 

clear, clc

err = 1;

order = 1;

while err > 0.000000001

syms x;

approx = taylor(exp(x),x,'Order',order);

 

x = 0.05;

 

approx = eval(approx);

err = abs(exp(0.05) - approx);

order = order + 1

end