1. If we plan to find a root for the function f(x) = x^2-2x +1 by using the foll

Question

1. If we plan to find a root for the function f(x) = x^2-2x +1 by using the following methods:
(i) Bisection method,
(ii) Regula Falsi (False position),
(iii) Secant,
(iv) Newton’s method.
Explain what happens when we apply the above methods. Can we successfully obtain the answer by those methods? Will the convergence acceptable? State your arguments as formal as possible!

2.For the same function in the previous question, can we use the modified Newton’s method to find the answer? State your reason as clear as possible.

Explanation / Answer

According to chegg policy if question have more then 4 part solve using first 4.

(i) Bisection method:

Start with interval [0,1]

x2-2x+1=0

Let f(x)=x2-2x+1

f(1)=0, So Root of the equation  is 1.

(ii) Regula Falsi (False position):

x2-2x+1=0

Let f(x)=x2-2x+1

f(1)=0, So Root of the equation  is 1.

(iii) Secant:

x2-2x+1=0

Let f(x)=x2-2x+1=0

f(1)=0, So Root of the equation  is 1.

iv) Newton’s method:

x2-2x+1=0

Let f(x)=x2-2x+1

?f?(x)=6x2-2

f(1)=0, So Root of the equation  is 1

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