Question

Use a known maclaurin series to obtain the maclaurin series for the given function. f(x = 8x2 tan?1(7x3

Answer 1

Going out on a limb here and guessing that the function is


`f(x)=8x^2\tan^(-1)(7x^3)`

Please correct me if this isn't the case.

Recall that


`\tan^(-1)x=\displaystyle\sum_(n\ge0)((-1)^nx^(2n+1))/(2n+1)`

which converges for
`|x|<1`.

It follows that


`8x^2\tan^(-1)(7x^3)=8x^2\displaystyle\sum_(n\ge0)((-1)^n(7x^3)^(2n+1))/(2n+1)`

`=\displaystyle\sum_(n\ge0)(56(-49)^nx^(6n+3))/(2n+1)`