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1(a) Let f(x) = x – 5 cos(x). By calculating f(1) and f(2), show that there is an a e [1, 2] such that f(a) = 0. You should give your values of f to four significant figures. 1 and b = 2, the first two iterations of the bisection method for the function given (b) With a in part (a) are shown in the following table. Do two more iterations to find the missing values in the table which are denoted by ???.

1(a) Let f(x) = x – 5 cos(x). By calculating f(1) and f(2), show that there is an a e [1, 2] such that f(a) = 0. You should give your values of f to four significant figures. 1 and b = 2, the first two iterations of the bisection method for the function given (b) With a in part (a) are shown in the following table. Do two more iterations to find the missing values in the table which are denoted by ???.

Algebra & Trigonometry with Analytic Geometry
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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1(a) Let f(x) = x – 5 cos(x). By calculating f(1) and f(2), show that there is an a e [1, 2] such that f(æ) = 0. You should give your values of f to four significant figures. (b) With a = 1 and b = 2, the first two iterations of the bisection method for the function given in part (a) are shown in the following table. Do two more iterations to find the missing values in the table which are denoted by ???. bn f(æn) 1.1463 n An an 1 1 2 1.5 1 1.5 1.25 -0.3266 ??? ??? 3 ??? ??? ??? 4 ??? ??? ??? (c) For the function f of part (a), write down the corresponding Newton-Raphson method. Then take xo = 1 and do two iterations of this method. You should give your values of x1 and x2 to six significant figures.
Transcribed Image Text:1(a) Let f(x) = x – 5 cos(x). By calculating f(1) and f(2), show that there is an a e [1, 2] such that f(æ) = 0. You should give your values of f to four significant figures. (b) With a = 1 and b = 2, the first two iterations of the bisection method for the function given in part (a) are shown in the following table. Do two more iterations to find the missing values in the table which are denoted by ???. bn f(æn) 1.1463 n An an 1 1 2 1.5 1 1.5 1.25 -0.3266 ??? ??? 3 ??? ??? ??? 4 ??? ??? ??? (c) For the function f of part (a), write down the corresponding Newton-Raphson method. Then take xo = 1 and do two iterations of this method. You should give your values of x1 and x2 to six significant figures.
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