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Q. I would like you to use a fixed point method to solve the positive real...

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Advance Math

Q. I would like you to use a fixed point method to solve thepositive real quadratic root of 4 by solving h(x) = x^4 ? 4 = 0.The standard method manipulates h(x) = 0 into g(x) = x so that theiterative scheme becomes xn+1 = g(xn). The iterative scheme willconverge to the required solution if the root is in the intervaldefined by |g '(x)| < 1

(i) We begin by adding x to both sides of the equation to form x= x^ 3? 4+ x such that g(x) = x ^3 + x ? 4. Will the root be found?(ii) We now try adding ?2x to both sides of the equation to form?2x = x ^4? 4 ? 2x such that g(x) = ?1/ 2 (x ^4? 2x ? 4 ) Will theroot be found? (iii) What is the smallest value k that willguarantee convergence if we add ?kx to both sides of theequatio

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