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phosgene

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## Homework Statement

Recall that the Maclaurin series for sin(x) is [itex]\sum\frac{(-1)^{k}x^{2k+1}}{(2k + 1)!}[/itex].

Use this formula to find the Maclaurin polynomial P

_{5}(x) for f(x)=xsin(x/2).

## Homework Equations

## The Attempt at a Solution

I know that to approximate sin(x/2) with the Maclaurin polynomial for sinx, I just substitute x/2 for x. But for xsinx, since the Maclaurin series is approximating sinx, can I just substitute the series for sinx so that I get [itex]x\sum\frac{(-1)^{k}x^{2k+1}}{(2k + 1)!}[/itex]?