# This is a asymptotic problem

1. Apr 18, 2010

### hancock.yang@

1. The problem statement, all variables and given/known data
Find the complete asymptotic expansion of the function $$\sqrt{1+x^{6}}$$ - x$$^{3}$$lnx as x$$\rightarrow$$$$\infty$$ and x$$\rightarrow$$0.
In each case give the asymptotic sequence in decreasing orders of magnitude.

2. Relevant equations
I tried the Taylor Expansion about 0. But I don't know how to give in decreasing orders of magnitude.

3. The attempt at a solution