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Using differential nad linear approximation

  1. Oct 16, 2011 #1
    1. The problem statement, all variables and given/known data

    I just have a question regarding "estimating" the value of a function at a given point. Say we have a function [itex]f(x, y, z, w)[/itex] and we want to know the value of that function at [itex]f(1.99, 1.001, 8.02, 2.01)[/itex]

    Can we simply do the following:

    let [itex]f=f(2, 1, 8, 2)[/itex] and
    [itex]df=\frac{\delta f}{\delta x}dx+\frac{\delta f}{\delta y}dy+\frac{\delta f}{\delta z}dz+\frac{\delta f}{\delta w}dw[/itex]

    Then say:
    [itex]f(1.99, 1.001, 8.02, 2.01)=f(2, 1, 8, 2)(1-df)[/itex]

    ??? or is that completely wrong?
     
  2. jcsd
  3. Oct 17, 2011 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Almost. You can, by the way get [itex]\partial[/tex], which is what I think you meant rather that [itex]\delta[/itex], by using "\partial" in the LaTeX.

    But it is not "f(1- df)" , it is simply f- df. where df is the the partial derivatives at (2, 1, 8, 2) multiplied by dx= -0.01, dy=0.001, dz= 0.02, and dw= 0.01.
     
  4. Oct 17, 2011 #3
    Quick question, I always thought that the dx would be in percentage form. For example, (1-(1.99/2))=dx? Is it suffice to merely say dx=2-1.99?
     
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