# Using known Maclaurin series to approximate modification of original

1. Feb 20, 2013

### phosgene

1. The problem statement, all variables and given/known data

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

Use this formula to find the Maclaurin polynomial P5(x) for f(x)=xsin(x/2).

2. Relevant equations

3. 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 $x\sum\frac{(-1)^{k}x^{2k+1}}{(2k + 1)!}$?

2. Feb 20, 2013

### Dansuer

Re: Using known Maclaurin series to approximate modification of origin

yes you can

3. Feb 20, 2013

### CompuChip

Re: Using known Maclaurin series to approximate modification of origin

Yes. You can make that better if you now sweep the x inside the sum. You may also want to include the summation bounds as you can sometimes simplify further by shifting them.

4. Feb 20, 2013

### phosgene

Re: Using known Maclaurin series to approximate modification of origin

Sorry, didn't see that I forgot the bounds. It's supposed to be from n=0 to infinity. Thanks for the help guys :)