Complete two iterations of Newtons Method to approximate a zero of the functions using the initial given guess. Show all work.

Question

Complete two iterations of Newtons Method to approximate a zero of the functions using the initial given guess. Show all work. 

 

 

 

 

1. f(x) = x^2 - 5     ;     x1 = 2.2


2. f(x) = cos x      ;    x1 = 1.6

Answer 1

f(x) = x²-5      f'(x) = 2x

 

 

x1         f(x1)         f'(x1)   -f(x1)/f'(x1)

2.2        -0.16         4.4          .0364

2.2364   .001485   4.4728      -.000332

2.236068

 

f(x) = cos(x)    f'(x) = -sin (x)

 

x1              f(x1)            f'(x1)       -f(x1)/f'(x1)

1.6           .0292          .99957    -.0292

1.5708     .00000367   1.0000    -.0000037

1.5707963