Math $1510$

Written Assignment $4$

$4\mathrm{.}7-4\mathrm{.}9,5\mathrm{.}1-5\mathrm{.}5$

$5.$ Area Estimates. Find the following area estimates under the graph of the function $y=\frac{1}{x}.$ Give your answers as $($exact$)$ rational numbers.

a$)$ The midpoint estimate, $M_2,$ over the interval $1,7.$

b$)$ The midpoint estimate, $M_2,$ over the interval $4,28.$

c$)$ The midpoint estimate, $M_3,$ over the interval $1,7.$

d$)$ The midpoint estimate, $M_3,$ over the interval $4,28.$

e$)$ What do these estimates suggest about the area over the interval $1,7$ and the area over the interval $4,28?$