In this question we will approximate 82 with a rational

Last updated: 11/28/2023

In this question we will approximate 82 with a rational number a To use the linear approximation there is an obvious choice of function f x and point ao What are they f x 20 82 f x f x f xo x xo 999 b Use a linear approximation of f x at x xo to find a rational number approximating 82 Give your answer correct to at least 4 decimal places c Newton s Method finds roots zeroes of functions In order to use Newton s Method to approximate 82 we need a function g x such that 9 82 0 and g x has rational coefficients There is an obvious choice for g x For example to approximate 50 the obvious choice is g x x 50 to approximate 10 the obvious choice is g x x7 10 What is the obvious choice of g x to approximate 82 20 d Which integer zo makes g zo as close as possible to 0 on two iterations of Newton s Method using afa and n found above to approximate 82 Give your answers correct to at least 4 decimal plac