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Linear Approximation

  1. Jan 18, 2006 #1
    My book gives a formula for linear approximation of two independent variables, but I needed one for three. So I modified the formula given in the book, but I need someone to please just quickly see if it looks okay.

    Given:
    [tex]f(x,y)=z=f(x_0,y_0)+(\frac{\partial f}{\partial x} (x_0,y_0)) (x-x_0) + (\frac{\partial f}{\partial y} (x_0,y_0)) (y-y_0)[/tex]

    Modified:
    [tex]f(x,y,z)=f(x_0,y_0,z_0)+(\frac{\partial f}{\partial x} (x_0,y_0,z_0)) (x-x_0) + (\frac{\partial f}{\partial y} (x_0,y_0,z_0)) (y-y_0)+(\frac{\partial f}{\partial z} (x_0,y_0,z_0)) (z-z_0)[/tex]

    Does this look alright?
    It looks fine to me but I'm prone to overlooking glaring errors :grumpy:
     
  2. jcsd
  3. Jan 18, 2006 #2

    benorin

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    Homework Helper

    Beautiful.
     
  4. Jan 18, 2006 #3
    thanks a lot.
     
  5. Jan 18, 2006 #4

    Hurkyl

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    Gold Member

    When you have time, you might want to see if you can rigorously justify that expression!
     
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