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- 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.To find the root of the function f(x), write down the mapping function, g(x), for Newton’s method. Using x0 = π/3 as the initial guess, perform the first four iterations using Newton’s method. Also calculate the ratio |xn/xn−1| at every step. What does this ratio denote and what does its limiting value tell you about the convergence rate of Newton’s method?(a) Find a real root of the equation e^xtanx=1 by using iteration method and also apply Aitken's del^2 -process to accelerate the convergence. (b) FInd the value of the e^-1 when e=2.718 by using newton raphason method.
- Find the radius of convergence, R, and the interval of convergence, I. infinity signEn=1 xn/n2Find a representation as a series of powers for the function and determine the radius and interval of convergence.Find the values of x for which the series converges. (Enter your answer using interval notation.)
- Find the interval of convergence I of the series. (Enter your answer using interval notation.)find the first four nonzero terms in each of two power series solutions about the origin. Show that they form a fundamental set of solutions. What do you expect the radius of convergence to be for each solution? 9.y″ + (sin x)y = 0If a power series for some function y = g(x) has interval of convergence (−2, 2], is itpossible for the series for f′(x) to have interval of convergence [−2, 2]?Explain your answer.
- Find the interval of convergence. (Enter your answer using interval notation.) Sigma from n=0 to infinity equation: xn / n5 + 4If a power series cn(x + 3)^n converges conditionally when x = 3, find the radius of convergence. Explain your answer.a) Find the interval of convergence of the given. (Show detailed explanation or solution) b) Indicate the interval, also if it is _ < x < _.