help please:(

Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that R(x) → 0.]

for 8cos(x) at a=3pi

Question

help please:(

Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that R(x) → 0.]

for 8cos(x) at a=3pi

dan815 · Answer

hi

anonymous · Answer

hello!

dan815 · Answer

taylor series is off linear-->quadratic-->cub---->quartic and so on
approximations to hte next point

anonymous · Answer

right, i got that. however once i expand the taylor series my problem is simplifying it to a summation

dan815 · Answer

okay show me what u got

dan815 · Answer

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camerondoherty · Answer

Dan will teach you
He's the best

dan815 · Answer

okay so basically u can decompose the sin and cos

dan815 · Answer

and the coeffeicients infront of them as the summation of odd a even increments of n factorial

anonymous · Answer

so far i've gotten,

$$\frac{ -8(x-3\pi)^0} { 0! }+\frac{ 8(x-3\pi)^1} { 1! }-\frac{ 8(x-3\pi)^2} { 2! }+\frac{8(x-3\pi)^3} { 3! }$$

and so on.. what do i do from here?

camerondoherty · Answer

He's #2kewl4skewl

dan815 · Answer

okay eyah thats good

dan815 · Answer

so now rewrite that as a summation alterating negative sign so

dan815 · Answer

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