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Business Calculus with Excel

Appendix E Spreadsheet Skills introduced in chapter 7

This appendix accumulates the spreadsheet skills introduced in chapter 7 of this textbook.
The main skill in this chapter was to Construct a right-hand rule Riemann sum template We recount the example from the section 7.1.4. In the set-up of the example 7.1.6. We follow our standard practice of putting the question and answer in labeled areas at the top of the worksheet. We want to see the start a and end b of the interval, along with number of subintervals. The width of a subinterval is the width of the whole interval divided by the number of subintervals. The column \(x_n\) is for the x value at the right side of the n-th subinterval. We calculate the value of \(x_n\) by taking the starting point, \(a=x_o\text{,}\) and adding \(n\) times the width of a subinterval. We then evaluate the function at \(x_n\text{,}\) which we label \(f(x_n)\text{.}\) The area of the n-th rectangle is the height, or \(f(x_n)\text{,}\) times the width of the subinterval. The last column is the total area for the first n rectangles. The sum is taken from the top of the block (with a semi-absolute reference) to the current row. The area for 100 rectangles is our area estimate. Since we don’t want to have to look all over for our answer, we bring the area up to cell D2 with the OFFSET command. The command OFFSET(E6,B3,0) starts in cell E6, goes down B3 (the number of subintervals) rows, and goes over 0 columns. In our case, it finds the value in cell E106 and puts it in cell D2. A Screencast of the Riemann sum axample 7.1.5 is available.
The variant of right-hand Riemann summs is to Construct a midpoint rule Riemann sum template We recount the example from the section 7.2.5. In the set-up of the example 7.2.7 we added an extra colum for the midpoint. The midpoint is the right hand edge of the interval minus half the length of the subinterval. We then evaluate at the midpoint.
Excel and Sheets work identically with respect to setting up these templates.