$($a$)$ Find the approximations $T_{10}$ and $M_{10}$ for ${\displaystyle \underset{1}{\overset{2}{}}}29e^{\frac{1}{x}}dx.($Round your answers to six decimal places.$)$

$T_{10}=$

$M_{10}=$

$($b$)$ Estimate the errors in the approximations of part $($a$)$ using the smallest possible value for $K$ according to the theorem about error bounds for trapezoidal and midpoint rules. $($Round your answers to six decimal places.$)$

$|E_T|,$

$|E_M|,$

$($c$)$ Using the values of $K$ from part $($b$),$ 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 $0\mathrm{.}0001?$

For $T_{n^{\text{'}}}n=$

For $M_{n^{\text{'}}}n=$

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