Question

In: Advanced Math

Use Newton's method to find all solutions of the equation correct to eight decimal places. Start...

Use Newton's method to find all solutions of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations. (Enter your answers as a comma-separated list.)

4e-x2 sin(x) = x2 − x + 1

Solutions

Expert Solution

MATLAB Script:

close all
clear
clc

syms x
f = 4*exp(-x^2)*sin(x) - x^2 + x - 1; % f(x)
fd = diff(f); % f'(x)
tol = 1e-8;

% Plotting f(x)
xx = -2:0.01:2;
ff = subs(f, xx);
plot(xx,ff), xlabel('x'), ylabel('f(x)')

ic = 0.22;
[result] = my_newton(f,fd,ic,tol);
fprintf('Solution, x: %.8f\n', result)

ic = 1.08;
[result] = my_newton(f,fd,ic,tol);
fprintf('Solution, x: %.8f\n', result)

function [res] = my_newton(func,func_d,ic,tol)
res = ic;
while true
x_ = res;
res = res - subs(func, res)/subs(func_d, res);
if abs(x_ - res) < tol
break;
end
end
end

Plot:

Output:

Solution, x: 0.21916368
Solution, x: 1.08422462


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