Use Winplot, Google Docs, and possibly Microsoft Excel/Google Spreadsheets to create a document with two problems on it.
Consider the function \(y = 0.1 x^3 - \cos(x^2) - 0.5x + 2\) on \([-2,3]\).
Use Winplot to create a graph of the curve on the interval. Include the graph in the document.
Use Winplot to complete this table.
| Method | 2 | 5 | 10 | 100 | 1000 |
|---|---|---|---|---|---|
| Left endpoint | |||||
| Midpoint | |||||
| Right endpoint | |||||
| Trapezoidal | |||||
| Parabolic | |||||
| Random |
The instructor has a school website that receives thousands of hits each day. The hits column represents the number of hits (in thousands of hits per day) for that day.
| Date | Nov 1 | Nov 5 | Nov 8 | Nov 17 | Nov 18 | Nov 21 | Nov 30 |
|---|---|---|---|---|---|---|---|
| Hits | 43.398 | 71.863 | 43.841 | 60.835 | 77.347 | 70.385 | 36.982 |
Use the information to estimate the number of hits during the month of November 2013 using the five approaches given in the table. You may want to use a spreadsheet to speed up the calculations, although the data points are limited enough that you could do it by hand.
| Method | Estimate | Relative Error |
|---|---|---|
| Left endpoints | ||
| Right endpoints | ||
| Trapezoids | ||
| Minimums | ||
| Maximums |
The total count for the month was 1714.325 thousand hits (1.714 million). The relative error is usually given as a percent. You take the estimate minus the actual value and then divide by the actual value. Finally, convert that into a percent.