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Math Help - maclaurin series what am i doing wrong?

  1. #1
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    Unhappy maclaurin series what am i doing wrong?

    hey guys ive attached a jpg with the question:

    f(x)= sin3x
    f'(x)= 3cos3x
    f''(x) = -3.3sin3x
    f'''(x) = 3.3.3cos3x

    I took a=0 and began to input it into the derivations:

    f(0) = 0
    f'(0) = 3
    f''(0) = 0
    f''' (0) = 27

    but when i put it into the maclaurin series i get 3x + 27x^3/3!
    shudnt i get the original formula again? what have i done wrong?
    Attached Thumbnails Attached Thumbnails maclaurin series what am i doing wrong?-maclaurin-series-q1.jpg  
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  2. #2
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    Your question does not make sense. You are making a trigonometric function into an infinite polynomial. Why would you expect any visual similarity?

    Besides the sign error on the 3rd derivative, you have it.
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  3. #3
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    so the answer i have given is the answer that the question expects?
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  4. #4
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    I would suggest an expansion about x = 0 of

     f(x) = f(0)+f'(0)x+\frac{f''(0)x^2}{2!}+\frac{f'''(0)x^3}  {3!}+\dots =  \sin(3\times 0)+3\cos(3\times 0)x-\frac{9\sin(3\times 0)x^2}{2!}-\frac{27\cos(3\times 0)x^3}{3!}+\dots
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  5. #5
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    Not quite. You need to do two more things:

    1) Fix the error in the 3rd derivative.

    2) Find the 5th derivative so that you can add the 3rd non-zero term. You've only two.
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