Use newton’s Method to approximate the given number to eight decimal places. (Show your work for the first two iterations of Newton’s Method, and afterward you can simply list the rest)

Question

(𝑎) ⁷√(1000) (𝑏) ln (600)

Answer 1

(a)

The solutions to y = x^7-10 are needed...

y' = 7x^6

Newton's method says the solution is 1.389495494373137637135

correct to 21 digits

root_7(10000) = roo_7(10^3) = 10^(3/7) = [10^(1/7)]^3 = 1.389495494373137637135 ^3

y = e^x-600 is the function whose solution is needed...

y' = e^x

Newton's method says 6.396929655216146368849

The onine calculator is at the following website

( slashes replace with underscores)

keisan dot casio dot com _ exec _ system _ 1244946907