Each equation has one real root Use Newtons Method to approx

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

Solution

(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