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la). Show that f(x)=(x-2)² – Inx =0 has at least one root between 1 and 2. b). Use bisection method to find the first 3- approximations of a solution of the equation f(x) = (x– 2)² – In x = 0 [1,2]. (3- digit rounding) P. f(P,) 1 3 c)Find the minimum number of iterations required to achieve an approximation of a solution of the equation f(x) = (x- 2)² – In x = 0 in [1,2] with an accuracy of 10

la). Show that f(x)=(x-2)² – Inx =0 has at least one root between 1 and 2. b). Use bisection method to find the first 3- approximations of a solution of the equation f(x) = (x– 2)² – In x = 0 [1,2]. (3- digit rounding) P. f(P,) 1 3 c)Find the minimum number of iterations required to achieve an approximation of a solution of the equation f(x) = (x- 2)² – In x = 0 in [1,2] with an accuracy of 10

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
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la). Show that f(x)= (x– 2)² – In x = 0 has at least one root between 1 and 2. b). Use bisection method to find the first 3- approximations of a solution of the equation f(x) = (x- 2)² – In x = 0 [1,2]. (3- digit rounding) b, Pn f(p,) 1 3 c)Find the minimum number of iterations required to achieve an approximation of a solution of the equation f(x)= (x– 2)² – In x = 0 in [1,2] with an accuracy of 104 d)In the graph given below, locate the position of second approximation p, obtained by Bisection method. 1 0.8 0.6 0.4 a = 0.4 b=1.2 0.2 -0.4 -0.2 0.2 0.4 0.8 1 1.2 1.4 1.6 -0.2 -0.4
Transcribed Image Text:la). Show that f(x)= (x– 2)² – In x = 0 has at least one root between 1 and 2. b). Use bisection method to find the first 3- approximations of a solution of the equation f(x) = (x- 2)² – In x = 0 [1,2]. (3- digit rounding) b, Pn f(p,) 1 3 c)Find the minimum number of iterations required to achieve an approximation of a solution of the equation f(x)= (x– 2)² – In x = 0 in [1,2] with an accuracy of 104 d)In the graph given below, locate the position of second approximation p, obtained by Bisection method. 1 0.8 0.6 0.4 a = 0.4 b=1.2 0.2 -0.4 -0.2 0.2 0.4 0.8 1 1.2 1.4 1.6 -0.2 -0.4
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