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Math Help - Taylor series analysis question

  1. #1
    LHS
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    Taylor series analysis question



    Hi, could anyone help me with part b of this question, part a I have completed, however I seem to be drawing a blank on the second part
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    Behold, the power of SARDINES!
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    Quote Originally Posted by LHS View Post


    Hi, could anyone help me with part b of this question, part a I have completed, however I seem to be drawing a blank on the second part
    Hint: Just use the definition of the derivative to get

    \displaystyle f'''(x)=\lim_{h \to 0}\frac{f''(x+h)-f''(x)}{h}= -\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}=-f,(x)

    Now use the above to find the forth derivative then you can probe that

    f^{n+4}(x)=f^{n} for all n \in \mathbb{N}

    Then use this relationship to find the Taylor series for this function.

    Just FYI this is the function \cos(x)
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  3. #3
    LHS
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    Ah thank you, probably should have seen that, but that's what ten hours and about a gram of caffeine do to you. Cheers
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