Answer:
x₃=1.599997=1.6
Step-by-step explanation:
f(x)=cos x, x₁=1.6
[tex]f'(x)=\frac{d}{dx}cos\ x\\=-sin\ x[/tex]
First iteration
At x₁=1.6
f(x₁)=f(1.6)
=cos(1.6)
=-0.0292
f'(x₁)=f'(1.6)
=-sin(1.6)
=-0.9996
[tex]\frac{f(x_1)}{f'(x_1)}=\frac{-0.0292}{-0.9996}\\=0.0292\\x_2=x_1-\frac{f(x_1)}{f'(x_1)}=1.6-(0.0292)\\\therefore x_2=1.5708[/tex]
[tex]f(x_2)=f(1.5708)\\=cos 1.5708\\=0.000003\\f'(x_2)=-sin1.5708\\=-1\\x_3=x_2-\frac{f(x_2)}{f'(x_2)}=1.6-\frac{0.000003}{-1}\\\therefore x_3=1.599997=1.6[/tex]
