# Thread: taylor series higher dimensions

1. ## taylor series higher dimensions

I have absolutely no idea how you do these. the text book is too complicated and doesnt really explain it very well. could anyone give me a hand doing some of these in detail so i can do the rest myself for a test tomorrow?

Find the Taylor series expansions of each of the following functions of
x and y about the points given:

i) $\displaystyle f(x,y)=sinh(x)cosh(y)$ about $\displaystyle (x,y)=(0,0)$
ii)$\displaystyle f(x,y)=ln(1+x+y)$ about $\displaystyle (x,y)=(0,0)$

thanks

2. Does the text book not give a formula?

The Taylor series for a function f(x,y) about $\displaystyle (x_0, y_0)$ is
$\displaystyle \sum_{i=0}^\infty\sum_{j= 0}^\infty\frac{1}{(i+ j)!}\frac{\partial^{i+j}f(x_0,y_0)}{\partial x^i\partial y^j}(x- x_0)^i(y- y_0)^j$.

3. Originally Posted by HallsofIvy
Does the text book not give a formula?

The Taylor series for a function f(x,y) about $\displaystyle (x_0, y_0)$ is
$\displaystyle \sum_{i=0}^\infty\sum_{j= 0}^\infty\frac{1}{(i+ j)!}\frac{\partial^{i+j}f(x_0,y_0)}{\partial x^i\partial y^j}(x- x_0)^i(y- y_0)^j$.
yeah thats the formula it gives but im really struggling implementing it. i just dont know what to do where and am getting really confused with it. if you could show me a step by step procedure on how to do these kinds of things easiest that would be amazing, real life saver test tomorrow

thanks