restart;
f := x->x^2-2;

df := diff(f(x), x);

A := x-f(x)/df;

phi := unapply(A, x);

x0 := 2;

x1 := phi(x0);

x2 := phi(x1);

x3 := phi(x2);

f(x3);

x4 := phi(x3);

f(x4); 

x5 := phi(x4); 

f(x5); 

evalf(x5); 

evalf(sqrt(2)); 

Digits := 40; 

evalf(x5); 

evalf(sqrt(2)); 

f := x->x^2-sin(x);

plot(f(x), x = 0 .. 2); 

df := diff(f(x), x); 

A := x-f(x)/df; 

phi := unapply(A, x); 

x0 := 1; 

x1 := phi(x0); 

x2 := phi(x1); 

x2a := evalf(x2); 

x3 := phi(x2a); 

x4 := phi(x3); 

x5 := phi(x4); 

x6 := phi(x5);