Limits of Riemann Sums
2. Consider the function \( f(x) \) and the interval \( [a,b] \) given by your instructor. Use the interactive SageMath window below to answer in your lab report the following questions.
(a) Complete the table in your lab report with the values of the required left, right, and middle Riemann sums.
(b) Does the list of middle Riemann sums appear to be approaching a limit? If so, what is your best guess for the value of this limit? If not, explain why not. Record your answers in your lab report.
(c) Generate 5 different random Riemann sums using the number of rectangles specified in your lab report. To generate one such sum, select the Random button under “Method.” To generate further random sums, click on the RUN AGAIN button. Record these numbers in your lab report.
(d) Compute the average of the five randomized sums you generated in part (c) and compare this average to your estimate for the limit of the collection of midpoint Riemann sums from part (b). You may use the SageMath cell below the interactive SageMath window to compute the average.