$($a$)$ Find the approximations $T_4$ and $M_4$ for ${\displaystyle \underset{1}{\overset{2}{}}}33e^{\frac{1}{x}}dx.($Round your answers to six decimal places.$)$

$T_4=$

$M_4=$

$($b$)$ Estimate the errors in the approximations of part $($a$).($Round your answers to six decimal places.$)$

$|E_T|$

$|E_M|$

$($c$)$ How large do we have to choose $n$ so that the approximations $T_n$ and $M_n$ to the integral in part $($a$)$ are accurate to within $0\mathrm{.}0001?$

$T_n,n=$

$M_n,n=$