6-Assuming that the following fixed-point iteration converges 3 Ik+1= 17 (2) 2 a-√3 c-√√5 Ik + to which fixed point will it converge? b-√√√3 d-None
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- 6. Consider xn+1 = (1/3)(2xn - 9/xn2). Does it converge for any nonzero initial point? If so, to what values?To find the unique solution p^∗ ∈ [0, 1] of the equation x^3 + 6x^2 − 4 = 0, rewrite the equation in the fixed-point form x = g(x) with two different choices of g, such that the sequence {pn} from the fixed-point iteration pn = g(pn−1) is expected to converge to p^∗ when p0 is sufficiently close to p^∗(but not equal to p^∗). Explain why your choices of g would work.determine the radius and convergence of E n=1 5xn/3n2
- I had tried Xn=(-1)^nbut since 2((-1)^n)^n =2(-1)^(n^2) (which is not always 1) it doesn't converge to some real number.Prove that the sequence {cn} converges to c if and only if the sequence {cn- c} converges to 0.Which one of the following methods always converges while finding the root of f(x) = 0.
- Prove that the sequence (Xn)=(−1)n+1 does not converge to any real numberSolve Σ 0 to ∞ ((n! • x^n)/ n^n) for x = e and x = -e and explain whether each point converges or divergesNote that the following three Fixed-Point Iterations converge to √2. A) x → (1/2)x + 1/x B) x → (2/3)x + 2/(3x) C) x → (3/4)x + 1/(2x) Which of the following rank correctly the ones that converge from fastest to slowest? Group of answer choices a.) B)→A)→C)B)→A)→C) b.) For all, the convergence speed are same. c.) A)→B)→C)A)→B)→C) d.) C)→A)→B)C)→A)→B) e.) C)→B)→A)
- 8.7.22. Prove that the Taylor series converges to f(x) by showing that .a. Find a real root of the equation e\power{x}tanx=1by using iteration method and also apply Aitken's Δ\power{2} -process to acceleratethe convergence. b Find the value of e\power{-1} where e=2.718 by using newton raphson.Find the first 4 non-zero terms of (1+3x)^(1/4) centered at x=0. what is the radius of the convergence?