Finding the Taylor Polynomial f4 for sin(2x) at x=pi/4.

[seto6]

Homework Statement

find the taylor polynomial f4 for f(x)=sin(2x) and a=pi/4

Homework Equations

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

The Attempt at a Solution

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

is this right?

 

[Susanne217]

Homework Statement

find the taylor polynomial f4 for f(x)=sin(2x) and a=pi/4

Homework Equations

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

The Attempt at a Solution

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

is this right?

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!

 

[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

 

[Susanne217]

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

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