Chapter 9, Problem 57RE

(a)

To determine

The Riemann sum which approximates the total expense over maintenance for

next two years and the integral for Riemann sum approximates for large values of $n$, where

$M\left(t\right)$ is the annual rate of maintenance expense at time $t$ such that $0\le t\le 2$ is divided into $n$

subintervals, with endpoints $t_0=0,t_1,t_2,\mathrm{...},t_n=2$.

(b)

To determine

The Riemann sum which approximates the present value of the total expense

over maintenance for the next two years and the integral for Riemann sum approximates for large

values of $n$, where $M\left(t\right)$ is the annual rate of maintenance expense at time $t$ such that $0\le t\le 2$

is divided into $n$ subintervals, with endpoints $t_0=0,t_1,t_2,\mathrm{...},t_n=2$ and $10\%$ is the annual

interest rate compounded continuously.