Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    Homework Helper

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

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    When you have time, you might want to see if you can rigorously justify that expression!
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook