Newton's Method will converge to a true solution if you have a good initial approximation. If you don't it may not converge at all. Consider, for example, the equation f(x) = x(x – 1)(x+1) =x' –x = 0. Obviously, the solutions are -1, 0, 1. x= If we start Newton's Method with xo being close to one of these solutions we will get convergence to that solution. On the other hand, note that f'(x) = 3x² – 1 is zero when 1 x=± V3 Thus the tangent will be horizontal in those two cases, and New- ton's can't even be carried out. In this problem we’ll investigate what happens in the contrived case that V5 5 You can enter xo into WeBWorK as sqrt(5)/5. Try it: Xo = Now do your computations using exact arithmetic, and you'll rec- ognize a pattern: X1 = X2 X3 X4 = || |||| ||

Q: Without using technology, please solve for the following equations for z exactly. (a) sin 2z = cosz…

A: (a) Given trigonometry equation is: sin2x=cosx To find the value of x in 0≤x≤π

Q: The approximation of the root x' of the function f(x) = x³e* - 1 accurate to within 10-2 using…

A: In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac…

Q: Find the following using the table below. 1 3 4 f(x) f' (æ) g(æ) g'(æ) 4 3 2 1 1 3 4 1 3 4 3 1 h'(1)…

A:

Q: Solve the 4nitial Value psoblem 2(5) 4(K+2)² ln Gx?) 2dy dx %3D

A: Given initial value problem is  2dydx+25xy=4x+22lnx2 using the initial condition y1=0. We can…

Q: The following information is given. f(3) = 5, f(3) = -2, g(3)=2, g(3) = 7 f(5)=3, f'(5)=-1,…

A:

Q: Find f by solving the initial-value problem. f'(x) = 7e* – 6x³, ƒ(0) = 5 -

A:

Q: Solve initial value problem f'(x) = x³ – 8x2 + 16x + 1;f(0) = 0.

A:

Q: Use the finite-difference approach to solve y"=-2-(A+x<)y for boundaries y(-1)=0 and y(1)=0 with…

A:

Q: We have an equation called (*) where e-x = x3 where we have that x is an element of R. Where the…

A:

Q: Use boundary conditions (2) in u (x, 1) = X (t) T (1) are, u (0, t) = X (0) T (t)=0 And u (L, t) = X…

A:

Q: Calculate two iterations of Newton's Method to approximate a zero of the function using the given…

A:

Q: We have an equation called (*) where e-x = x3 where we have that x is an element of R. Where the…

A: Given

Q: -3 Let A = 4 Find etA and use it to solve ' = A with initial conditions x(0) = |. -2

A: We find etA first and then use it we find the solution of x'=Ax

Q: Q3/B/By using Newton-Raphson method, then the value of the root of the equation x = cos (2x) when x,…

A:

Q: A ball with mass 1.5 kg is thrown upward with initial velocity 2 m/s from the roof of building 15 m…

A: The mass of the ball is :m=1.5 kg Initial velocity is :The initial height of the ball is :Consider…

Q: At time t = 0, a storage tank is empty and begins filling with water. For t > 0 hours, the depth of…

A:

Q: The following information is given. f(3) = 5, f(5)= 3, 11. (a) Find H'(3) if H(x) = g(f(x)). 11. (b)…

A:

Q: PROBLEM NO. 6 GIVEN: f(x) = cos(x)-√√9-x² Using NEWTON'S METHOD, determine new estimate after 2nd…

A:

Q: For each of h(x) find h'(x): (a) h1(x) = . Hint: Use Quotient Rule.

A: Proceed as shown below

Q: Find the general antiderivative of each function. (can check by taking the derivative) F(X)= 12x3…

A:

Q: Solve the differential equation dy dr e-"(1 - y)? in general. Then sketch solution trajectories…

A: For the solution follow the next steps.

Q: If f(x) = cos(2x), which of the equations below describes the average rate of change of f(x) over…

A:

Q: g(x) :|(1-/1- (a+1)²)da -x2 Solve for g(0) and g'(V2)

A:

Q: 40. It is easy to check that f(z) = r - 4z has two roots. Find these two roots using Newton's method…

A:

Q: Mu= x 0.85 x fc' x axbx (d-a/2) 266000000 (486-a/2) = 0.9 x 0.85 x 21 x ax 366 x a= uknown "x" Using…

A: The main objective is to estimate the x value by using Newton Raphson method.

Q: dy (2x + 3y) (y – x) dx ||

A: GIVEN