Chapter 9.4, Problem 34E

(a)

To determine

To prove: The number of liters of blood flowing past the monitoring point during the $i\text{th}$ time interval is $\approx \left(R/60\right)\Delta t$

(b)

To determine

To prove: The quantity of dye flowing past the monitoring point during the $i\text{th}$ time interval is $\approx c\left(t_i\right)\left(R/60\right)\Delta t$

(c)

To determine

If all the dye will have flowed past the monitoring point during the $22$ second, then why $D\approx \left(R/60\right)\left[c\left(t_1\right)+c\left(t_2\right)+\cdots +c\left(t_n\right)\right]\Delta t$ and the approximation improves as $n$ gets large.

(d)

To determine

The value of $R$ and conclude that $D={\displaystyle \underset{0}{\overset{22}{\int }}\left(R/60\right)}c\left(t\right)dt$