# Thread: Approximate Expression from Taylor Expansion: f(x)=(a/x)^(12)-2(a/x)^6

1. ## Approximate Expression from Taylor Expansion: f(x)=(a/x)^(12)-2(a/x)^6

Given:
f(x)=(a/x)12-2(a/x)6
Use a Taylor Expansion about x=a to obtain an approximate expression for f(h), where h=x-a, to a second order in h.

So I've found:
f'(x)=12a6/x7-12a12/x13
f''(x)=156a12/x14-84a6/x8

And evaluated at x=a:
f(a)=-1
f'(a)=0
f''(a)=72/a2

This gives the expansion:
f(x)=36(x-a)2/a2-1

I thougt at this point, I could then do f(h) or f(x-a) by substituting x=h or x=x-a, but the answer is expected to be only in terms of h, so I am not sure what to do next.
Any help would be much appreciated

2. If the answer is "expected to be only in terms of h" then use h= x-a which is what the problem told you: $\frac{36}{a^2}h^2- 1$.

3. Which is what I thought, but I can't have an a term apparently.