Question

The Taylor series expansion for ax is: Write a MATLAB program that determines ax using the Taylor series expansion. The program asks the user to type a value for x. Use a loop for adding the terms of the Taylor series. If cn is the nth term in the series, then the sum Sn of the n terms is . In each pass calculate the estimated error E given by . Stop adding terms when . The program displays the value of ax. Use the program to calculate: (a) 23.5 (b) 6.31.7 Compare the values with those obtained by using a calculator.

Answer 1

Answer: (a). 11.3137

(b). 22.849

Explanation:

Provided below is a step by step analysis to solving this problem

(a)

clc;close all;clear all;

a=2;x=3.5;

E=10;n=0;k=1;sn1=0;

while E >0.000001

cn=((log(a))^n)*(x^n)/factorial(n);

sn=sn1+cn;

E=abs((sn-sn1)/sn1);

sn1=sn;

n=n+1;

k=k+1;

end

fprintf('2^3.5 from tailor series=%6.4f after adding n=%d terms\n',sn,n);

2^3.5 from tailor series=11.3137 after adding n=15 terms

disp('2^3.5 using calculator =11.3137085');

Command window:

2^3.5 from tailor series=11.3137 after adding n=15 terms

2^3.5 using calculator =11.3137085

(b)

clc;close all;clear all;

a=6.3;x=1.7;

E=10;n=0;k=1;sn1=0;

while E >0.000001

cn=((log(a))^n)*(x^n)/factorial(n);

sn=sn1+cn;

E=abs((sn-sn1)/sn1);

sn1=sn;

n=n+1;

k=k+1;

end

fprintf('6.3^1.7 from tailor series=%6.4f after adding n=%d terms\n',sn,n);

disp('6.3^1.7 using calculator =22.84961748');

Command window:

6.3^1.7 from tailor series=22.8496 after adding n=16 terms

6.3^1.7 using calculator =22.84961748

cheers i hope this helped !!!