# Homework Help: Taylor polynomialneed help bad!

1. Apr 21, 2010

### seto6

1. The problem statement, all variables and given/known data
find the taylor polynomial f4 for f(x)=sin(2x) and a=pi/4

2. Relevant equations
sin(x)=((-1)^n)(x^(2n+1))/((2n+1)!)

3. The attempt at a solution

so replace x with 2x?
you get ((-1)^n)(2x)^(2n+1)/(2n+1)!)

is this right?

2. Apr 21, 2010

### Susanne217

Its a good thing to present it the right way...

You know the formula right?

$$\sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!} \cdot (x-a)^{n} = \sum_{n=0}^{\infty} \frac{f^{(4)}(\frac{\pi}{4})}{4!} \cdot (x-\frac{\pi}{4})^{4}$$

which you simply expand as show in your Calculus book which then inturn gives the right answer!

3. Apr 21, 2010

### seto6

i see i have to center it at pi/4 but this is ((-1)^n)(2x)^(2n+1)/(2n+1)!) centered at 0 so i have to derive it sin(2x) using center pi/4 right

thanks man

4. Apr 21, 2010

### Susanne217

you welcome :) Generally do you have the Edwards and Penny Calculus Bible? You find the whole definition and example in there :)