Math Calculus
posted by Soojung .
Use Newtonâ€™s Method with initial approximation x1 = 2 to solve the equation x5 +x= 6 . Go to x3,
and tell me how good you think the approximation is. Round all answers to 3 decimal places.

let f(x) = x^5+x6
newton's method says
x_{n+1} = x_{n}  f(x_{n})/f'(x_{n})
f'(x) = 5x^4 + 1
so x2 = x1  f(x1)/f'(x1)
= 2  28/81
= 1.65432
then x3 = 1.65432  .209237
= 1.44508
x4 = 1.3685
x5 = 1.35942
x6 = 1.359304105
x7 = 1.359304086
x8 = 1.359304086 Ok then !!!