Exercises

1. For each function listed, do the following. Look at the results of rightbox and leftbox for n = 5 and 10. You do not need to include these plots in your report. Find the upper and lower sums (be sure to indicate which is which) with n = 50, 100, and 200. Based on this information alone, make a guess as to the value of A. Explain the basis for your guess.
   1. on the interval .

   2. on the interval .

2. For each function given in Exercise 1, do the following. Look at the results of middlebox for n = 5 and 10. You do not need to include these plots in your report. Find the midpoint approximation with n = 50, 100, 200. Now what would you guess is the value of A? Explain your guess.

3. The following problems refer to the given in Exercise 1. Both questions below can be answered through the use of appropriate Maple commands. Note that the command

   h:= diff(g(x), x$2);

   defines the Maple expression h to be the second derivative of . Also note that the solve command can be used with inequalities.

   1. If is used to approximate A, what accuracy is guaranteed by the error bound formula? Be sure to state what value of N you chose and explain how you picked it.

   2. What is a reasonable n to use if 6-place accuracy is desired? That is, if