1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Quick Linearization Question

  1. Oct 2, 2006 #1
    I am linearizing the function [tex]f(x,y,z) = tan^{-1}(xyz)[/tex] at the point (1,1,1).

    Since [tex]f(x_0,y_0,z_0)= \frac{\pi}{4} + \pi*n[/tex] should I just take the first value or do I have to carry all the solutions through the linearization process?

    Um, anybody remember this? I can put up some work if it helps.

    [tex]L(x,y,z) = \Delta f = f_x \Delta x + f_y \Delta y + f_z \Delta z[/tex]

    So

    [tex]L(x,y,z) = f(x_0,y_0,z_0) + f_x(x-x_0) + f_y (y-y_0) + f_z (z-z_0)[/tex]

    where [tex]f_x = \frac{\partial f}{\partial x}[/tex] (and f_y and f_z)

    So does [tex] L(x,y,z) = \frac{\pi}{4} +\pi n + \frac{1}{2}[(x-1)+(y-1)+(z-1)] [/tex]
    ???
     
    Last edited: Oct 2, 2006
  2. jcsd
  3. Oct 2, 2006 #2
    Surely somebody must know. I have doubts that I should include the general solutions, because that would be a strange linearization. I'm not really sure though, since the general solutions would be just as valid, unless I am overlooking something.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Quick Linearization Question
Loading...