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Math Help - maclaurin series

  1. #1
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    maclaurin series

    or this question, i found that my coefficient of x^4 is wrong... after applying the maclaurin series formula, i would get the coefficient of X^4 is -5/96.... but the exact ans is -1/96... can anyone check which part is wrong?
    Attached Thumbnails Attached Thumbnails maclaurin series-dsc_0118-2-1-.jpg   maclaurin series-dsc_0117-2-1-.jpg  
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  2. #2
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    Re: maclaurin series

    maclaurin series-clipboard01.jpg

    the first vector is the derivatives of $\sqrt{\cos(x)}$ unevaluated.

    the second vector is the above evaluated at $x=0$

    the third vector is the second further scaled by $k!$ and are thus the coefficients of the Maclaurin series.

    you can figure out where you went wrong.
    Thanks from delso
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    Re: maclaurin series

    hi, can you do it in the form of y^2 = cos x ? it would be easier for me to check where's my mistake. thanks!
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    Re: maclaurin series

    Quote Originally Posted by delso View Post
    hi, can you do it in the form of y^2 = cos x ? it would be easier for me to check where's my mistake. thanks!
    why would you do it that way?

    There are many places to use implicit differentiation. This isn't one of them.
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    Re: maclaurin series

    maybe what you said is correct! if i use your method, there'll be less differentation will be performed
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    Re: maclaurin series

    for this, my coefficient of x^4 which is 8/4! = 1/3 .. but the ans should be 13/24... can you tell me which part contain mistake? or any shortcut to do this question rather than perform so many times of implicit differentiation?maclaurin series-dsc_0119-4-1-.jpgmaclaurin series-dsc_0119-5-2-.jpg
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    Re: maclaurin series

    Quote Originally Posted by romsek View Post
    why would you do it that way?

    There are many places to use implicit differentiation. This isn't one of them.
    sorry, i couldnt understand your working after -1/2 (sin x )/(cos x )^-0.5 ... can you check my working that i've post earlier please..
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    Re: maclaurin series

    maclaurin series-clipboard01.jpg

    same format as last time.

    letting $u=e^x-1$ and expanding about $u=0$ might save you some writing.
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  9. #9
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    Re: maclaurin series

    for the question y= cos x )^0.5 , to find the coeffeicient of x^3 and X^4 , must using the equation of proven part to proceed... can you do it from that part please?
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