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June 12th, 2012, 10:30 AM  #1 
Senior Member Joined: Apr 2012 Posts: 106 Thanks: 0  Taylor polynomial with two variables
Dear all, I need to approximate the following term: with a Taylor polynomial of the first degree. How do we do that? 
June 12th, 2012, 11:58 AM  #2 
Global Moderator Joined: May 2007 Posts: 5,973 Thanks: 431  Re: Taylor polynomial with two variables
Expand each factor using binomial {(1+.02)^3 and (1.03)^2} multiply out and keep the first nonzero term after 1.

June 12th, 2012, 08:15 PM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,131 Thanks: 437 Math Focus: Calculus/ODEs  Re: Taylor polynomial with two variables
Let The differentials of the independent variables are: The total differential of the function is: A Taylor polynomial of the first degree is linear, so we may use: Let: 
June 13th, 2012, 01:05 AM  #4 
Senior Member Joined: Apr 2012 Posts: 106 Thanks: 0  Re: Taylor polynomial with two variables
Thanks a lot!


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polynomial, taylor, variables 
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