Determine h if V = 1.1535 m³ and r= 1m using Fixed point iteration on the given convergent equation. Compute the convergence, g(x). Show solution and complete the table of results. V πh² (3r — h) 3 Xn 1 Xn+1 h = h³ + 3V/π 3r
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- Does the sequence {(n^(3)+6n)/(e^(n))} converge or diverge? Why? If it converges, find its limits.Note 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)For which a does 1/n(ln(n))^a converges? Justify your answer.
- 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.Determine whether the sequence xn =√(5+3n+7n2)/(4n2-n+2), converges or diverges. If it converges, find the limitThe equation f(x) = x3 – x2 – 10x – 8 has a root within the interval 3.8 ≤ x ≤ 4.5. If the prespecified tolerance of 0.001 is required, find this root using both the Bisection and Newton-Raphson Method. Compare the rate of convergence on theroot between the two methods.
- decide if {xn}∞n=1 converges or not: (a) xn = 1/nFind the first few coefficients (c0, c1, c2, c3, c4,) and radius of convergence (R).Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is inconclusive.∑n=1∞enn!ρ=limn→∞|an+1an|= (Enter 'inf' for ∞.) ∑n=1∞enn! is:A. convergentB. divergentC. The Ratio Test is inconclusive