$(16$ points$)$ Complete the table, recending the Riemann Sums accurate to ten$-$thoesandits place to approximate the following integrat: ${\displaystyle \underset{e}{\overset{t}{}}}{e}^{-x}dx.$

$\backslash$table$[[$Number of Subintervals,Ieff$-$Hand Ricmann Sum,Right$-$hand Riemann Sum$],[8,,],[16,,],[32,,],[64,,],[128,,],[256,,],[512,,],[1024,,]]$

$(3$ points$)$ Do the values of the left$-$hand Riemann sums approach a limiting value as the number of subinaervals gets larger? If so$,$ what is that value? Explain using complete sentences.

$(3$ poine$)$ Ane the right$-$hasd Rieman sums larger or smaller than the exact anea under the curve? Write your answer as a complete sentence.

$(4$ points$)$ Explate why the righe$-$hand Rienann sums increase as the number of rectangles increases. Write your mswer as a complete serience.

$(3$ points$)$ Do the values of the right$-$hand Riemann sums approach a limiting value as the nomber of sibintervals get larger? If so$,$ what is that value? Write your answer as a complete sentence.