Explain how, in general, riemann sum approximations to the area of a region under a curve change as the number of subintervals increases.

As you increase the subintervals the area will be closer and closer to the real value. In other words your approximation gets better.

As you increase the intervals, there will be more rectanagles and the added area of these rectangles are converging towards the actual area under the curve.

whole numbers.

step-by-step explanation:

we are given the average monthly rainfall (in millimeters) model r(m) for the years 1900-2009 as a function of the month number m.

as we can see m is taken for the number of months for years 1900-2009.

we know that number of months can't be a negative number or decimal number or a fraction.

so, the number of months could be only positive whole numbers.

therefore, whole numbers is more appropriate for the domain of r.