How to Calculate Taylor Approximations for Given Function and Parameters?

[royzizzle]

Homework Statement

find the 2nd, 3rd, and 6th degree taylor approximation of:

f(x) = 10(x/2 -0.25)⁵ + (x-0.5)³ + 9(x-0.75)²-8(x-0.25)-1

for h = 0.1 to h = 1, with $$\Delta$$h = 0.05

and where x_o=0; and x = h

Homework Equations

N.A

The Attempt at a Solution

I just need to know what exactly they are trying to ask. I know how to do Taylor expansion. but they don't define their variables and I don't know what x0 and h are supposed to be. Where is the approximation going to be centered? at h or at x0?

and what is the interval for h supposed to be?

 

[TheoMcCloskey]

It does look poorly written without any other context. But, upon reading again, I would *guess* (not generally recommended) they are asking for (various degress of) the Taylor expansion of the expression about xo = 0 evaluated for various values of x=h where h varies .10, .15, .20,.25, ..., 1.0 (ie, 19 values of h)

Thus, I think they want:
19 numerical values for the 2nd degree Taylor approximation (about xo=0)
19 numerical values for the 3rd degree Taylor approximation (about xo=0)
19 numerical values for the 6th degree Taylor approximation (about xo=0)