Question

1.    Solve cos(x)=2x, using fixed point iteration to 5 decimal places             

Do 5 iterations.    Solve , using fixed point iteration to 5 decimal places       

Answer 1

Given that $cos(x)=2x$

Applying fixed iteration method:

$x=\frac{cos(x)}{2}\\ \therefore x_{n+1}=\frac{cos(x_n)}{2}\\$

Take $x_0=1\\$

So,

$x_1=\frac{cos \ 1}{2}=0.27015\\ x_2=\frac{cos(x_1)}{2}=\frac{cos(0.27015)}{2}=0.48186\\ x_3=\frac{cos(x_2)}{2}=\frac{cos(0.48186)}{2}=0.44306\\ x_4=\frac{cos(x_3)}{2}=\frac{cos(0.44306)}{2}=0.45172\\ x_5=\frac{cos(x_4)}{2}=\frac{cos(0.45172)}{2}=0.44984\\$