Question

Each equation has one real root. Use Newton’s Method to approximate the root to eight correct decimal places. (a) x5 + x = 1 (b) sin x = 6x + 5 (c) ln x + x2 = 3

**MUST BE DONE IN MATLABE AND SHOW CODE

Answer 1

(a)

root = 0.754877666246693

Matlab code:

format long;
x=5;
h = (x^5 + x -1) /(5*(x^4) + 1 );
i = 1;  
while(abs(h) >= 0.00000001)
h = (x^5 + x -1) /(5*(x^4) + 1 );
x = x - h;
i=i+1;
end
x

(b) root = -0.970898923504256

Matlab code:

format long;
x=5;
h = (sin(x) - 6*x - 5) /(cos(x) -6 );
i = 1;  
while(abs(h) >= 0.00000001)
h = (sin(x) - 6*x - 5) /(cos(x) -6 );
x = x - h;
i=i+1;
end
x

c) root = 1.592142937058094

Matlab code:

format long;
x=5;
h = (log(x) + x^2 - 3) /((1/x) + 2*x );
i = 1;  
while(abs(h) >= 0.00000001)
h = (log(x) + x^2 - 3) /((1/x) + 2*x );
x = x - h;
i=i+1;
end
x