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Taylor Series expansion of x and y about points. Watch

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    Taylor series is probably my worst subject so far. I have a question that asks me to find the Taylor series expansion of this function of x and y about the points given;

     f(x,y) = 2x^2 - xy - y^2 - 6x -3y +5 about  (x,y) = (1,-2)

    One thing I'm confused about is that it's finite, it only "survives" (terrible phrasing I know) until the third differential, so can there really be a series? Can anyone point me in the right direction? I'm terrible at Taylor Series.
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    There can be a series, it just won't be infinite.
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    Actually, you can imagine it as an infinite series, just with every term after the one it terminates at as zero
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    (Original post by ljfrugn)
    There can be a series, it just won't be infinite.
    (Original post by Serano)
    Actually, you can imagine it as an infinite series, just with every term after the one it terminates at as zero
    Ah right, thanks. Unfortunately my lecture notes only gives information on infinite series and even then only gives two examples, so I'm not exactly sure how to approach the question. I know that;

     f_x = 4x - y - 6



f_{x^2} = 4



f_{x^3} = 0









f_{y} = -x - 2y -3 



f_{y^2} = -2



f_{y^3} = 0



    Soooooo


     f_{x}(1,-2) = 0



f_{x^2}(1,-2) = 4



f_{x^3}(1,-2) = 0









f_{y}(1,-2) = 0



f_{y^2}(1,-2) = -2



f_{y^3}(1,-2) = 0

    And to use the formula

     \frac {f_{{x^m}{y^n}}(x_0,y_0)}{m!n!}(  x-x_0)^m(y-y_0)^n

    But exactly how do I notice a series from the differentials?
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    Bump, still don't really understand. (I've checked google and things).
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    http://en.wikipedia.org/wiki/Taylor's_theorem

    Did you look at this, under "Taylor's theorem for several variables"? The multi-index notation they use might seem a bit alien - if you find it confusing then I'll try to find a different site or write it out in a more explicit fashion.
 
 
 
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