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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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. TI F3 T The Weather Channel On DELL F4 144 F5 ►11 F6 → F7 F8 500 F9 F10 F11
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. TI F3 T The Weather Channel On DELL F4 144 F5 ►11 F6 → F7 F8 500 F9 F10 F11
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