determination of e^x using Taylor series

hello, i'm new with matlab. i want to solve this equation by using matlab A=B*e^(0.2356X1+0.1869X2+0.0969X3) where A=1e8 and B=1e6 how can i find X1, X2, and X3 values ?

thanks

Answer 1

[Dimitris Kalogiros]

clear; clc;

syms A B x_1 x_2 x_3
syms a_1 a_2 a_3

%definition of equation
myEq= A==B*exp(a_1*x_1+a_2*x_2+a_3*x_3)

% solve equation.
% choose one variable and consider the others as parameters
% which taking arbitrary values
mySol=solve(myEq, x_1 )

% replace the values of parameters
A=exp(8);  B=exp(6);
a_1=0.2356; a_2=0.1869; a_3=0.0969;

subs(mySol)

If you run the script:

Answer 2

[Meshari Alqahtani]

Dimitris, thank you for answering my question but why you use the A=exp(8); B=exp(6); what are the 8 and 6 ?

[Dimitris Kalogiros]

" where A=1e8 and B=1e6 "

1e8 means e^8 or 10^8 ?

whatever it means , you can substitude the proper value into my script

[Meshari Alqahtani]

got it. thanks

[Meshari Alqahtani]

it mean 10^8

Answer 3

[Meshari Alqahtani]

Dimitris,

how can i get the value of the X1, X2, and X3 as number ?and i just wanna rewrite the equation for you again, because i confused you with exponantial and the e power.

 A = B*exp(0.2356X1+0.1869X2+0.0969X3)

where:

A=1x10^8
B=1x10^6

does matlab can solve this problem maybe with Taylor series or any loop method to find the X values as numbers.

thank you again

[Walter Roberson]

You have one equation in three variables. There are an infinite number of solutions.

 A = B*exp(0.2356X1+0.1869X2+0.0969X3)

then

   A/B = exp(0.2356X1+0.1869X2+0.0969X3)

then

log(A/B) = 0.2356X1+0.1869X2+0.0969X3

The left hand side is a constant, so this is the equation for a plane in three space, and any point on the plane satisfies the equation.

[Dimitris Kalogiros]

Walter is right.

In my script, you have to give values at x2, x3 and calculate the value for x1. So you would have the solution (x1, x2, x3)

clear; clc;
syms A B x_1 x_2 x_3
syms a_1 a_2 a_3

%%definition of equation
myEq= A==B*exp(a_1*x_1+a_2*x_2+a_3*x_3)

%%solve equation.
% choose one variable and consider the others as parameters
% which taking arbitrary values
mySol=solve(myEq, x_1 )

%%replace the values of parameters
A=1E8;  B=1E6;
a_1=0.2356; a_2=0.1869; a_3=0.0969;
mysol=subs(mySol)

%%An example: lets find a solution
x_2=1
x_3=2
x_1=vpa(subs(mysol))

[Meshari Alqahtani]

what if i have the value of 0.2356X1+0.1869X2+0.0969X3=9.4851. if there is any way to get solution for x1, x2, and x3 by using taylor series or loop method, i'm really try to find any way by using mat lab to get the Xs values if i have the value of a1 a2 a3 A and B?

[Torsten]

Did you read Walter's comment ? It answers your question.

[Walter Roberson]

taylor series is useless for this purpose.

If you are working over real numbers, there are zero solutions if A/B is negative, and there are an infinite number of solutions otherwise. You can choose random values for any two of the three values and directly calculate the third value.

For example,

x12 = randn(2,1) .* rand(2,1) .* 10000;  %about +/- 30000-ish
X1 = x12(1); X2 = x12(2);
X3 = (9.4851 - 0.2356*X1 - 0.1869*X2) ./ 0.0969;

%cross check
0.2356*X1 + 0.1869*X2 + 0.0969*X3

In the test I just did, the result of the cross-check was 9.48509999999987 instead of 9.4851 "exactly", a difference of 1.24344978758018e-13 . You will not generally be able to get exact solutions due to floating point round-off. You could reduce the discrepancy by reducing the range of random values used.

Answer 4

[Apisara]

Find percent(relative) errors of approximating e^x using Taylor series expansions with n=0,1,2,3,4 at x=5

[Steven Lord]

This is not an answer to the original question. You should ask it as a separate question using the Ask button at the top of this page.

But since this sounds like a homework assignment, when you ask that separate question please show us the code you've written to try to solve the problem and ask a specific question about where you're having difficulty and we may be able to provide some guidance.

If you aren't sure where to start because you're not familiar with how to write MATLAB code, I suggest you start with the free MATLAB Onramp tutorial to quickly learn the essentials of MATLAB.

If you aren't sure where to start because you're not familiar with the mathematics you'll need to solve the problem, I recommend asking your professor and/or teaching assistant for help.