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Linear Approximations

  1. Oct 26, 2014 #1
    1. The problem statement, all variables and given/known data
    Use an appropriate linear approximation to estimate the value [itex] (0.97)^{3}(2.02)[/itex]. Write your answer as a simplified decimal.


    2. Relevant equations
    Linearization:
    [itex] L(x,y) = f(a,b) + \frac{\partial z}{\partial x}(a,b)(x-a) + \frac{\partial z}{\partial y}(a,b)(y-b) [/itex]

    3. The attempt at a solution
    I am a little confused on this one about how to get going, but once I get started this shouldn't pose to much of a problem. I was thinking (I came here to confirm this thought) that I could define a function:
    [itex] z = x^{3}y [/itex]
    Then I would take:
    [itex] a = 1 \hspace{2 mm} b = 2 [/itex]
    Then I would go from there and formulate the linearization. I just wanted to see if this was the right way to proceed or not..
     
    Last edited: Oct 26, 2014
  2. jcsd
  3. Oct 26, 2014 #2

    Mark44

    Staff: Mentor

    Looks like you're mostly on the right track, but your partials aren't right.

    Since z = f(x, y), the partials you want are ##\frac{\partial z}{\partial x}## and ##\frac{\partial z}{\partial y}##. It might be that you wrote them upside down inadvertently.
     
  4. Oct 26, 2014 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Best policy: just go ahead and do it.
     
  5. Oct 26, 2014 #4
    Ah, thank you...I just wrote it down wrong by accident :)
     
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