Problem:
Find the second order expansion about $x = 3$ of the composition $f(g(x))$ for $f(x) = \tan (x)$ and $g(x) = $\sqrt{x^2}$
Answer:
$(x-3)^2 \left(1+\tan ^2(3)+3 \left(\tan ^3(3)+\tan (3)\right)\right)+(x-3) \left(3+3 \tan ^2(3)+\tan (3)\right)+3 \tan (3)$
{'source': 'AMPS', 'file': 'amps/mathematica/calculus/series_compose/29248.txt'}