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Math Help - taylor series higher dimensions

  1. #1
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    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) 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
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  2. #2
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    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.
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    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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