3. Apply Newton's method to f(x) = x³-5 using initial guess x0 = 1.5. a) Calculate x1, x2, and x3 up to 5 decimal places. b) Do the same calculations using initial guess x0 = 1. c) Find the difference between x3 for the different initial guesses. d) Solve x3 = 5 on your calculator and find the error from your estimate and the actual answer.
3. Apply Newton's method to f(x) = x³-5 using initial guess x0 = 1.5. a) Calculate x1, x2, and x3 up to 5 decimal places. b) Do the same calculations using initial guess x0 = 1. c) Find the difference between x3 for the different initial guesses. d) Solve x3 = 5 on your calculator and find the error from your estimate and the actual answer.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Transcribed Image Text:3. Apply Newton's method to f(x) = x³-5 using initial guess x0 = 1.5.
a) Calculate x1, x2, and x3 up to 5 decimal places.
b) Do the same calculations using initial guess x0 = 1.
c) Find the difference between x3 for the different initial guesses.
d) Solve x3 = 5 on your calculator and find the error from your estimate and the actual
answer.
4. Apply Newton's method to f(x) = 1-x sin x using an initial guess x0 = 7.
a) Calculate x1, x2, and x3 up to 5 decimal places.
b) Do the same calculations using initial guess x0 = 3.
c) Graph f(x) in Desmos and explain why your calculations led you to different answers.
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