# Taylor's Series problem help

1. Nov 29, 2009

### suryakalpo

1. The problem statement, all variables and given/known data
Expand f(x)=x^3 + 3x^2 +15x -10 in powers of x-1

2. Relevant equations

Taylor's Series, Maclaurin's series

3. The attempt at a solution

I dont know how to start...I do have an idea of both the theorems but dont know how to apply it to this situation.

plz help...sem exams in a week's time!!!

2. Nov 29, 2009

### zcd

Re: Series

x-1 means centered about x=1; the polynomial has only 4 relevant derivatives so just use the formula

3. Nov 29, 2009

### HallsofIvy

Staff Emeritus
Re: Series

One way to do this, without using Taylor's series, is to let u= x-1 so that x= u+1. Your polynomial becomes $(u+1)^3 + 3(u+1)^2 +15(u+1) -10$. Expand that in powers of u and, finally, replace u by (x-1) to get the polynomial in powers of x-1.

But simpler is to use the Taylor's series formula:
f(a)+ f(a)(x-a)+ f(a)/2(x-a)^2+ f(a)/3! (x-a)^3+ ...

4. Nov 29, 2009

Re: Series

thanks