Find the approximations $L_n,R_{n^{\text{'}}},T_{n^{\text{'}}}$ and $M_n$ for $n=5,10,$ and $20.$ Then compute the corresponding errors $E_{L^{\text{'}}}{E}_{R^{\text{'}}}{E}_{T^{\text{'}}},$ and $E_M.($Round your answers to six decimal places.

You may wish to use the sum command on a computer algebra system.$)$

${\displaystyle \underset{0}{\overset{1}{}}}7x{e}^{x}dx$

What observations can you make? In particular, what happens to the errors when $n$ is doubled?

As $n$ is doubled, $E_L$ and $E_R$ are decreased by a factor of about

$,$ and $E_T$ and $E_M$ are decreased by a factor of about