$(35$ Points$)$ After determining the $6^{th}$ order Taylor polynomial for the function $f(x)=\frac{2lnx+e^x}{x^3-3}$ around the point $x=2,$ by using this Taylor polinomial find actual error in approximation of $f(x)$ at $x=9\mathrm{.}42$ in format long.

Your answer:

$14\mathrm{.}812239147060131$

$2\mathrm{.}351789529731735e+06$

$7\mathrm{.}351774717492588e+06$

$7\mathrm{.}321774717492588e+06$