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Question

PROBLEM to apply Newton's Root Approximation Method to.


Consider the functions g(x)

= x3 ; h(x) = -3x+6

Apply Newton's Method to approximate x value intersection of these two graphs.


A. Please begin your first guess of x1 = 1, calculate up to x3 value.

B. Your title should include YOUR NAME: Newton

C. Naturally, I am also looking for a use able URL as well.

D. A graph zooming in on the point of intersection would be excellent as well.

         

SOLUTION: Set 

Call the new function f(x)=


                 x value                                   f'(x)=                                                        x[n] - {f(x) / f'(x)}

                                            f(x)=                                    x[n+1]=x[n]-f(x[n]) /f '(x[n])

ti-84              L1                   L2               L3                           L4                              L1 - L4 ... L5

    n              x[n] ... L        f(x[n])             f ' (x[n])            f(x[n])/f ' (x[n]) = y3              New guess

                                          = y1 ... L2     = y2 ... L3        = y1/y2 ..L4

    1                             1        

    2          

    3                   Final Solution    


Include a URL

calc 10.png

Top Answer

g(x) = x 3 h(x) = -3x + 6 g(x) = h(x) x 3 =+ 6 = 0 or , x 3 + 3 x - 6 = 0 f(x) = x 3 + 3 x - 6 f'(x) = 3 x 2 + 3 x 1 = 1 ,... View the full answer

newt3a.png

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