Question

Please use matlab to solve the question.

1. The following infinite series can be used to approximate e*: 2 3! n! Prove that this Maclaurin series expansion is a special case of the Taylor series (Eq. 4.13) with Xi = 0 and h a) x. b) Use the Taylor series to estimate f(x) e* at xH1 1 for x-0.25. Employ the zero-, first-, second- and third-order versions and compute the letlfor each case. Take the true value of e10.367879 for computing E

Answer 1

Hi,

The answer to your question is

a)

clc%clears the console
clear all%clears the history
close all%closes all opened files
syms f(x) sum(x) F(x)
f(x)=exp(x);
F=f;
xi=0;
sum(x)=0;
for i=0:10
sum=sum+F(xi)*((x-xi)^i)/factorial(i);
F=diff(f);
end
sum​

b)

clc%clears the console
clear all%clears the history
close all%closes all opened files
syms f(x) sum(x) F(x)
f(x)=exp(-x);
F=f;
xi=0.25;
sum(x)=0;
for i=0:3
sum=sum+F(xi)*((x-xi)^i)/factorial(i);
F=diff(F);
fprintf('Value of %d order version of exp(-%f) is %.20f and true relative error corresponding to it is %.20f\n',i,1,eval(sum(1)),abs(0.367879-eval(sum(1)))/0.367879);
end

Revert in case of any queries

Thanks.