Assuming that the following fixed point iteration converges x n+1 to which fixed point will it converge? OAVS O B.2 O D. None of the above
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- find the longest interval in whichthe following initial value problem is guaranteed to have a unique solution.(t + 1)g′′−√(16 −t^2)g′+ g = −t^3, g(−2) = 2, g′(−2) = −3.Consider the DEdy/dt = ((y −3)^(2/3))/(t −2 ).At each initial condition, determine if the Existence and Uniqueness Theorem guarantees the exis-tence of a unique solution. If so, what is the largest time interval on which the solution is guaranteed?If not, are we able to make any conclusions from the theorem?(a) y(4) = 0(b) y(1) = 3Solve Σ 0 to ∞ ((n! • x^n)/ n^n) for x = e and x = -e and explain whether each point converges or diverges
- 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)Which one of the following methods always converges while finding the root of f(x) = 0.Find values of C1 and C2 so that the given functions will satisfy the prescribed initial conditions.
- The instructions say to verify that the specified function is a solution of the given initial-value problem. I'm having issues doing both 31 and 33.The function g( x ) = π + 0.5sin(x/2 ) has a unique fixed point on [0 , 2π]. Estimate number of iterations needed to achieve an accuracy 10-7 , if we start with an initial guess Xo = π.If a root of f(x) = 0 lies in the interval [a, b], then find the minimum number of iterations required when the permissible error is E.
- Find the third iteration value of an extremum (maximum/minimum value) of if a = 5, b = 0.5, and c = 5 using Newton's Method with an initial guess value of x = - 4.32. Approximate the root of the following function first using the bisection method and then using method of falsi position with the stopping condition |(x)| <8 x10^-4 .?(x) = x^3+2x^2+10x-20, [1, 2] .Which method converges faster to the solution?Find all values ofxfor which ∞∑n=1 (3x)^n converges.