taylor series higher dimensions

**situation** · December 5th 2010, 06:07 AM

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

thanks

**HallsofIvy** · December 5th 2010, 07:28 AM

Does the text book not give a formula?

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

**situation** · December 5th 2010, 07:37 AM

Originally Posted by HallsofIvy

Does the text book not give a formula?

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

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

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