use a maclaurin series to obtain the maclaurin series for the given function f(x)= (sinx)^2 hint use (sinx)^2 = 1/2(1-cos2x)

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- May 4th 2009, 10:21 PMtwilightstrMaclaurin series
use a maclaurin series to obtain the maclaurin series for the given function f(x)= (sinx)^2 hint use (sinx)^2 = 1/2(1-cos2x)

- May 4th 2009, 10:25 PMTheEmptySet
- May 4th 2009, 10:37 PMGamma

Basically this amounts to finding the maclaurin series for cos(u) since then you can just put in a 2x for u (then multiply by your 1/2 scalar and subtract from 1/2). Note this trick works because the radius of convergence for this series turns out to be infinite, more care should in general be used.

let

f(u)=cos(u) f(0)=1

f'(u)=-sin(u) f'(0)=0

f"(u)=-cos(u) f"(0)=-1

f"'(u)=sin(u) f"'(0)=0

and repeat.

so:

so finally you see:

Think you can take her from here?