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A12. Consider the equation cos"(z) – 1 = 0. (a) Show graphically that (1) has a unique solution z for 0< r< 1. (b) Use the method of bisection to find an approximate solution z in the interval [0, 1] that is accurate to one decimal place. (c) Re-write (1) in the form z f(x), and use the method of fixed point iteration to find a better solution that is accurate to three decimal places.

A12. Consider the equation cos"(z) – 1 = 0. (a) Show graphically that (1) has a unique solution z for 0< r< 1. (b) Use the method of bisection to find an approximate solution z in the interval [0, 1] that is accurate to one decimal place. (c) Re-write (1) in the form z f(x), and use the method of fixed point iteration to find a better solution that is accurate to three decimal places.

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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A12. Consider the equation -I= 0. (a) Show graphically that (1) has a unique solution z for 0 < r< 1. (b) Use the method of bisection to find an approximate solution z in the interval (0, 1] that is accurate to one decimal place. (c) Re-write (1) in the form z f(x), and use the method of fixed point iteration to find a better solution that is accurate to three decimal places.
Transcribed Image Text:A12. Consider the equation -I= 0. (a) Show graphically that (1) has a unique solution z for 0 < r< 1. (b) Use the method of bisection to find an approximate solution z in the interval (0, 1] that is accurate to one decimal place. (c) Re-write (1) in the form z f(x), and use the method of fixed point iteration to find a better solution that is accurate to three decimal places.
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