Question

derivative of power function

f(x) = 3/(x2−x−12)

Answer 1

do i need to take the derivative or antiderivative or none

Answer 2

do you need to differentiate f ?

Answer 3

im trying to get the power series representation and then interval of convergence

Answer 4

i was able to get (-3*49)/4 * 1/(1-(2x-1)^2)

Answer 5

oh yeah its around the center x=1

Answer 6

you expansion Taylor series ?

Answer 7

im trying to get this into geometric series form

Answer 8

about center x=1

Answer 9

I think
x^2-x-12=(x-4)(x+3)
3/(x^2-x-12)=a/(x-4)+b/(x+3)
with a=3/7, b=-3/7
\[3/7/(x-4)=3/7(1/(x-1)\sum_{n=0}^{\infty}[3/(x-1)]^{n}\]

Answer 10

with b/(x+3) similar

Answer 11

WOW I figured out that i did wrong!! i didnt recognize that x^2-x-12 was the same as (x-4)(x+3) i know what to do now i have to do partial frac. then i can solve it