Consider A function f(x)= x³ - 7x² + 4x + 12. Construct two different fixed point functions g(x) such that f(x) = 0. (a)
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- 2. Determine the highest real root of f(x) = 2x³ - 11.7x² +17.7x-5 a. Graphically b. Fixed-point iteration method (three iterations, xo =3). Note: Make certain that you develop a solution that converges on the root.3. Consider the equation f(x) = x³ - 2x² – 11x + 12 on the interval [1.78, 8.25]. (a) Find the minimum number of iterations required to find the root of the given equation within the error bound of 1 x 10-3. (b) Show 5 iterations using the Bisection Method to find the root of the above function within the interval [1.78, 8.25].Use simple fixed-point iteration to locate the root of f(X) = 2sin(√x) - x
- identify the coordnates of any local maximum or minmum values of the function y=(x+3)2/ e2xLet f(x) = x² – 4x – 5. (a) Find Newton's method formula Pn = g(Pn-1). (b) Start with po = 5.1 and find p1 and P2. Use Horner's method for any polynomial evaluations. (c) Is the sequence converging quadratically or linearly? Explain your answer.4. Consider the function, f(x) = x³ = x² - 9x +9. Answer the following: State the exact roots of f(x). (a) (b) Construct three different fixed point functions g(x) such that f(x) = 0. (Make sure that one of the g(x)'s that you constructed converges to at least a root). (c) (d) Find the approximate root, x, of the above function using fixed point iterations up to 4 significant figures within the error bound of 1 × 10-³ using xo = 0 and any fixed point function g(x) from part(b) that converges to the root(s). Find the convergence rate/ratio for g(x) constructed in previous part and also find which root it is converging to?
- 1. Determine the highest real root of f(x) = 2x³ - 11.7x² +17.7x - 5. Also, compute for Ea- a. Graphically b. Fixed-point iteration method (five iterations,x, = 3). Note: Make certain that you develop a solution that converges on the root. c. Newton-Raphson Method (five iterations, x, = 3).2. Consider the function g(x) = 5 - 6/x a- Show that the function g(x) has a fixed point in the interval [2.5,3.5]. b- Find a root using Fixed Point Iteration. Use po = 2.6, to calculate the relative error.It has been found that a worker new to the operation of a certain task on the assembly line will produce P(t) items on day t, where P(t) = 24 - 24 e -0.31 How many items will be produced on the 1st day, and what is the maximum number of items, according to the function, the worker can produce? The worker will produce items on the first day. (Round to the nearest whole number.) The maximum number of items the worker will produce is (Round to the nearest whole number.) Question Viewer Enter your answer in each of the answer boxes. Escribe aquí para buscar hp
- Find the long run behavior of each of the following functions. If the function goes to ∞ or -∞ enter INFINITY or- INFINITY respectively. (a) As →∞, 10(0.4) (b) Ast-∞, 15(2.8) - (c) As t→∞, 0.2(1-(0.3)¹)→Find the root of f(x) = In(x/2) + 8x with Fixed Point Iteration method. - In () Take g (x) and the starting point as po = 0.15 Iterate four times. Take the precision as four digits by applying rounding methods.Suppose that the weekly sales S of a product are given by er Sup 20t S(t) = thousand dollars, t2 + 25 where t is the number of weeks since sales began. Suppose that the product has only been on sale for 15 weeks, so 0 < t< 15. Over what time interval are sales increasing? Enter your answer using interval notation, for example, something like [2, 8). What are the maximum weekly sales during this period? thousand dollars.