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.