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Find three nonzero terms of the Maclaurin series of the function

$f(x)={3/5} tan5x/x$

Using the maclaurin series i found them to be..

$3/5+x^2/25+2x^4/25$

Is this correct? If not what is the answer so I can find out where i went wrong. Im pretty sure its wrong

Thanks for any help

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It seems to be wrong.

Consider $$\tan(y)=y+\frac{y^3}{3}+\frac{2 y^5}{15}+O\left(y^7\right)$$ Replace $y$ by $5x$.

I am sure that you can take it from here.

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  • $\begingroup$ once ive replaced y do I just simplify? $\endgroup$ – someguy May 7 '16 at 8:55
  • $\begingroup$ I suppose that this is what to do. $\endgroup$ – Claude Leibovici May 7 '16 at 8:56
  • $\begingroup$ @ Claude Leibovici Ok I did that and im not sure my answer is correct, Im obviously missing something. $\endgroup$ – someguy May 7 '16 at 8:57
  • $\begingroup$ Ive returned two separate answers, which is correct? $3+25x^2+250x^4$ and $5+125/3*x^2+1250/5*x^4$ $\endgroup$ – someguy May 7 '16 at 9:02
  • $\begingroup$ You cannot get two different results. Write your rexpression using the result for $\tan(5x)$ from $\tan(y)$ with $y=5x$ and adjust the coefficients. One of your two answers is correct. Now, your turn ! $\endgroup$ – Claude Leibovici May 7 '16 at 9:17

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