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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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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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