what are the first three nozero terms of the Taylor series for f(x) = cos(x) about x = -Pi?

Printable View

- Feb 5th 2009, 04:34 PMmr_motivatortaylor series
what are the first three nozero terms of the Taylor series for f(x) = cos(x) about x = -Pi?

- Feb 5th 2009, 04:45 PMbob murray
The Taylor series expansion for a function f(x) about the point x = a is given by:

$\displaystyle f(x)=f(a)+(x-a)\frac{\partial}{\partial x} f(a) + \frac{(x-a)^{2}}{2!} \frac{\partial^{2}}{\partial x^{2}} f(a) + ...$

So in your case,

$\displaystyle f(x) = cos(x)$

and

$\displaystyle a = -\pi$

The process is just a matter of starting with the first term in the above series, inserting your function evaluated at $\displaystyle \pi$, and doing any necessary derivatives, etc, to see if it vanishes or not. Then proceed to the next term, and so on, until you have three nonvanishing terms. - Feb 5th 2009, 04:45 PMskeeter