Exercise 1.We consider the function f defined for any real r in the interval -1, 1], by f(x) = x +2x - 2.1. Prove that it exists exactly one root of f(x) = 0 in the interval [-1, 1].2. How much iterations of the bissection method we need to obtain a precision of 10.3. Make 2 iterations of the bissection method.Exercise 2.We consider the function g defined for any real r in the interval;, 0.65], by g(r) =1. Prove that the Fixed point algorithm r"+1equation r g(z) have a solution.= g(r"), with ro 0.65 is convergent and that the

1.We have given function f(x)=x3+2x-2 on [-1,1]f'(x)=3x2+2f'(x)=0⇒3x2+2=0x2=-23therefore , this is…

Exercise 1. We consider the function f defined for any real r in the interval [-1,1], by f(x) = x+2x-2. 1. Prove that it exists exactly one root of f(x) = 0 in the interval [-1, 1]. 2. How much iterations of the bissection method we need to obtain a precision of 10-3. 3. Make 2 iterations of the bissection method. Exercise 2. We consider the function g defined for any real r in the interval [;,0.65], by g(r) = r(1-2). 1. Prove that the Fixed point algorithm r"* = g(x"), with ro 0.65 is convergent and that the equation r g(x) have a solution. %3D

Exercise 1. We consider the function f defined for any real r in the interval [-1,1], by f(x) = x+2x-2. 1. Prove that it exists exactly one root of f(x) = 0 in the interval [-1, 1]. 2. How much iterations of the bissection method we need to obtain a precision of 10-3. 3. Make 2 iterations of the bissection method. Exercise 2. We consider the function g defined for any real r in the interval [;,0.65], by g(r) = r(1-2). 1. Prove that the Fixed point algorithm r"* = g(x"), with ro 0.65 is convergent and that the equation r g(x) have a solution. %3D

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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Question

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Exercise 1.
We consider the function f defined for any real r in the interval -1, 1], by f(x) = x +2x - 2.
1. Prove that it exists exactly one root of f(x) = 0 in the interval [-1, 1].
2. How much iterations of the bissection method we need to obtain a precision of 10.
3. Make 2 iterations of the bissection method.
Exercise 2.
We consider the function g defined for any real r in the interval
;, 0.65], by g(r) =
1. Prove that the Fixed point algorithm r"+1
equation r g(z) have a solution.
= g(r"), with ro 0.65 is convergent and that the

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