Question

For some constants A and B, the rate of production R(t), of oil in a new oil well is modeled by: R(t) = A + Be^(-t) * sin(2πt)

Where t is time in years, A is the equilibrium rate, and B is the "variability" coefficient.

a) Find the total amount of oil produced in the first N years of operation (where N is an integer)
b) Find the average amount of oil produced per year over the first N years (where N is an integer)
c) From your answer to part (b), find the average amount of oil produced per year as N→∞