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In this question, we will approximate 83 with a rational number. a)To use the linear approximation there is an obvious choice of function f(x) and point o. What are they? f(x) = Xo = ⠀ b) Use alinear approximation of f(x) at x = xo to find a rational number approximating 83. Give your answer correct to at least 4 decimal places. √83 x0 = c) Newton's Method finds roots (zeroes) of functions. In order to use Newton's Method to approximate 83, we need a function g(x) such that g(83) = 0 and g(x) has rational coefficients. There obvious choice for g(x). (For example: to approximate √50, the obvious choice is g(x)=x²-50; to approximate 10, the obvious choice is g(x)=x7 - 10.) What is the obvious choice of g(x) to approximate √83? g(x) = d) Which integer to makes g(xo) as close as possible to 0? ⠀ x1 = ⠀ f(x) f(x) + f'(xo)(x - xo) e) Use two iterations of Newton's Method (using g(x) and to found above) to approximate 83. Give your answers correct to at least 4 decimal places. ⠀ m

In this question, we will approximate 83 with a rational number. a)To use the linear approximation there is an obvious choice of function f(x) and point o. What are they? f(x) = Xo = ⠀ b) Use alinear approximation of f(x) at x = xo to find a rational number approximating 83. Give your answer correct to at least 4 decimal places. √83 x0 = c) Newton's Method finds roots (zeroes) of functions. In order to use Newton's Method to approximate 83, we need a function g(x) such that g(83) = 0 and g(x) has rational coefficients. There obvious choice for g(x). (For example: to approximate √50, the obvious choice is g(x)=x²-50; to approximate 10, the obvious choice is g(x)=x7 - 10.) What is the obvious choice of g(x) to approximate √83? g(x) = d) Which integer to makes g(xo) as close as possible to 0? ⠀ x1 = ⠀ f(x) f(x) + f'(xo)(x - xo) e) Use two iterations of Newton's Method (using g(x) and to found above) to approximate 83. Give your answers correct to at least 4 decimal places. ⠀ m

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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In this question, we will approximate 83 with a rational number. a)To use the linear approximation there is an obvious choice of function f(x) and point x. What are they? f(x) = xo = b) Use a linear approximation of f(x) at x = ïå to find a rational number approximating 83. Give your answer correct to at least 4 decimal places. 83≈ c) Newton's Method finds roots (zeroes) of functions. In order to use Newton's Method to approximate 83, we need a function g(x) such that obvious choice for g(x). - - (For example: to approximate √50, the obvious choice is g(x) = x² – 50; to approximate √10, the obvious choice is g(x) = x² – 10.) What is the obvious choice of g(x) to approximate ✓83? g(x) = d) Which integer x makes g(x) as close as possible to 0? x0 = x1 = X2 # e) Use two iterations of Newton's Method (using g(x) and found above) to approximate 83. Give your answers correct to at least 4 decimal places. || f() ~ f(xo)+f'(æo)(æ − xo) # ff 83) = 0 and g(x) has rational coefficients. There is an
Transcribed Image Text:In this question, we will approximate 83 with a rational number. a)To use the linear approximation there is an obvious choice of function f(x) and point x. What are they? f(x) = xo = b) Use a linear approximation of f(x) at x = ïå to find a rational number approximating 83. Give your answer correct to at least 4 decimal places. 83≈ c) Newton's Method finds roots (zeroes) of functions. In order to use Newton's Method to approximate 83, we need a function g(x) such that obvious choice for g(x). - - (For example: to approximate √50, the obvious choice is g(x) = x² – 50; to approximate √10, the obvious choice is g(x) = x² – 10.) What is the obvious choice of g(x) to approximate ✓83? g(x) = d) Which integer x makes g(x) as close as possible to 0? x0 = x1 = X2 # e) Use two iterations of Newton's Method (using g(x) and found above) to approximate 83. Give your answers correct to at least 4 decimal places. || f() ~ f(xo)+f'(æo)(æ − xo) # ff 83) = 0 and g(x) has rational coefficients. There is an
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