taylor series

**thehabsonice** · May 15th 2009, 06:18 PM

$cos (2x^2)-1/x^2$ at x=0
$f^(10)$ (0) = ?? (basically the 10th derivative)

I would appreciate it if someone could help me with this. I found C10 which is: $3^6/6!$ but I don't know what to do from there..

Thank you

**Jhevon** · May 15th 2009, 07:01 PM

Originally Posted by thehabsonice

$cos (2x^2)-1/x^2$ at x=0
$f^(10)$ (0) = ?? (basically the 10th derivative)

I would appreciate it if someone could help me with this. I found C10 which is: $3^6/6!$ but I don't know what to do from there..

Thank you

you should set out your problem more clearly. do you mean $\frac {\cos 2x^2 - 1}{x^2}$ or $\cos 2x^2 - \frac 1{x^2}$ ?

anyway, here's a hint: $\cos 2x^2 = \sum_{n = 0}^\infty (-1)^n \frac {(2x^2)^{2n}}{(2n)!}$

can you use that?

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