Find the approximations $T_{n^{\text{'}}}{M}_{n^{\text{'}}}$ and $S_n$ for $n=6$ and $12.$ Then compute the corresponding errors $E_T,E_M,$ and $E_S.($Round your answers to six decimal places. You may wish to use the sum command on a computer algebra system.$)$

${\displaystyle \underset{1}{\overset{4}{}}}\frac{32}{\sqrt[\phantom{2}]{x}}dx$

$\backslash$table$[[n,T_n,M_n,S_n$