1. In 1979 topical storm Claudette produced torrential rains when it hit Texas. The highest one-day total was reported in Alvin, Texas where 42 inches of rain fell in a single day. A rectangular region R of a National Weather Service isohyet map has been subdivided into grid areas, each 5 miles by 5 miles. The isohyets show levels of rainfall in inches within the 3 day period July 24-27, 1979. If the accumulated rain water somehow didn't flow away and formed a watery surface in the region R, isohyets will be the level sets of that surface. 20 (a) Using the grid provided, and upper and lower Riemann sums, find upper and lower estimates for the total amount of rain that fell over the region R during the three days. (b) What would happen to your upper and lower estimates if you used smaller grid sizes? Would they increase or decrease? Explain without explicitly calculating