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Math Help - taylor polynomial help!

  1. #1
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    taylor polynomial help!

    I don't really understand how to derive taylor polymomials for questions like these for example

    find the 3rd degree taylor polymomial about the origin of
    f(x,y) = (cos y) ln(xy+1)

    can someone please help and explain what the starting steps are
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  2. #2
    Senior Member
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    Re: taylor polynomial help!

    Quote Originally Posted by Kuma View Post
    I don't really understand how to derive taylor polymomials for questions like these for example

    find the 3rd degree taylor polymomial about the origin of
    f(x,y) = (cos y) ln(xy+1)

    can someone please help and explain what the starting steps are
    Do you know the Taylor series for cos(x) and ln(1+1) ?
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  3. #3
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    Re: taylor polynomial help!

    yes. Do I just substitute the terms of the question into the taylor series of cos x and ln 1+x?

    I was looking over some examples and that is what my instructor did. But what about a question like

    cos(xy)/[1 + y^2]

    there isn't a standard representation for the denominator.
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  4. #4
    Grand Panjandrum
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    Re: taylor polynomial help!

    Quote Originally Posted by Kuma View Post
    yes. Do I just substitute the terms of the question into the taylor series of cos x and ln 1+x?

    I was looking over some examples and that is what my instructor did. But what about a question like

    cos(xy)/[1 + y^2]

    there isn't a standard representation for the denominator.
    Expanding about 0:

    \frac{1}{1+y^2}=\frac{1}{1-(-y)^2}=1+(-y^2)+(-y^2)^2+...+(-y^2)^n+..

    CB
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