Expanding x³ + 3x² + 15x - 10 in powers of x-1

[suryakalpo]

Homework Statement

Expand f(x)=x^3 + 3x^2 +15x -10 in powers of x-1

Homework Equations

Taylor's Series, Maclaurin's series

The Attempt at a Solution

I don't know how to start...I do have an idea of both the theorems but don't know how to apply it to this situation.

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

 

[zcd]

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

 

[HallsofIvy]

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+ ...

 

[suryakalpo]

thanks