monkey*
  • monkey*
Find the first three iterates of f(x)=-3x-7 if x(o at the bottom)=-8 X1=17, x2=-58, x3=167 X1=21, x2=-61, x3=170 X1=-17, x2=58, x3=-167 X1=-21, x2=61, x3=-170
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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monkey*
  • monkey*
Help please.
monkey*
  • monkey*
Anyone?
xapproachesinfinity
  • xapproachesinfinity
What? i suppose this is newton's method appilication

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mathmate
  • mathmate
This is called a fixed point iteration, where you iterate \(x_{n+1}=f(x_n)\) Read about it here: https://en.wikipedia.org/wiki/Fixed-point_iteration
xapproachesinfinity
  • xapproachesinfinity
oh i see
mathmate
  • mathmate
For example, if f(x)=2x+1, and \(x_0\)=0, then \(x_1 = f(x_0) = 2(0)+1=1\) \(x_2 = f(x_1) = 2(1)+1=3\) \(x_3 = f(x_2) = 2(3)+1=7\) ....
monkey*
  • monkey*
Still a little confused about how you got everything.?
xapproachesinfinity
  • xapproachesinfinity
@mathmate that sequence is 2^n-1 divergent right?
mathmate
  • mathmate
Yes, in this case. It can be used to find roots, for example Solve f(x)=x^2-4x+3=0 We rearrange to have g(x)=x=(x^2+3)/4 with \(x_0\)=1.5 then g(\(x_0\))=1.3125 g(1.3125=1.18066 g(1.1866)=1.09849 ... eventually it will converge (slowly) to the root x=1.
mathmate
  • mathmate
@monkey* you can see another example I just posted previously. This second example converges slowly to x=1. The first example (and your question) will not converge, but that's normal.
monkey*
  • monkey*
Oh, okay. Thanks for explaining it.
mathmate
  • mathmate
You're welcome! :)
jdoe0001
  • jdoe0001
testing something

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