# Taylor series of two variable ?

1. May 28, 2009

### rclakmal

1. The problem statement, all variables and given/known data

I want to know that how to calculate the required number of terms to obtain a given decimal accuracy in two variable Taylor series .
In one variable case i know there is an error term R(n)=[ f(e)^(n+1)* (x-c)^(n+1)] / (n+1)! where 'e' is between x and c (c is the center value ) so if we want a 3 decimal place accuracy we can have the inequality below

R(n)<=5*10^(-4) then we can obtain particular ' n ' to have that accuracy

But i don't know how to use this in two variable case .please give some explanation or a good tutorial where i can learn it .

2. May 28, 2009

### HallsofIvy

Staff Emeritus
The corresponding formula for two variables is
$$R(n)= \sum_{i=0}^{n+1} \frac{\frac{\partial^{n+1} f(e)}{\partial x^{i}\partial y^{n+1-i}}(x-c)^{n+1}}{(n+1)!}$$

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