241lab - Lab Suggestions for Calculus I, Math 241/251...

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Lab Suggestions for Calculus I, Math 241/251 Getting Started. Introduce the students to the basics of DfW. Open the program, explain what you see, big white work page, line where you enter expression, pull down menus, tool bar, and special character pads. Next you can start doing things. Entering expressions and operations: 1. 3 + 5, enter, then simplify. 2. 1 / 3, enter, then show the difference between simplify and approximate. 3. Simplify ( - 1) 1 / 3 and solve x 3 = - 1. 4. Enter x 3 - a 3 x - a , illustrate the need of parentheses to get exactly this expres- sion. Notice, when you simplify the program performs a long division. 5. Square roots can be entered using the special character pad, or using the function sqrt .E v e n x - a x - a and x 1 / 3 - a 1 / 3 x - a are simplified by long division. 6. Mention the mathematical constants π , the Euler number e ,andthe factor = π/ 180 for converting degrees into radians on the pad for special characters. 7. Enter the equation x 3 - 5 x 2 - x + 5 = 0, and find its solutions al- gebraically using the command solve . You can solve other equations numerically. 8. DfW knows a lot of functions. Just type sin x ,tan x ,andy ouhav e the function to work with. The inverse functions are denoted by, e.g., asin x . You can find a long list of functions by going to the help index under Functions, Derive Functions. 9. You can use the substitute command to replace a variable by anything of your choosing. So, if you substitute a number, then you can evaluate a function at a point. 10. The program will implement some identities when you simplify, e.g., sin 2 x +cos 2
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Basic graphing: 1. Open a graphing window by clicking on the button with the sine curve on the tool bar. Click on Window, and tile vertically. Then you will have your algebra window and a graphing window. 2. In the algebra window, highlight a function which you like to graph, click on the button with the sine curve at the top of the graphing window. You will see the graph of the function. 3. Use the zoom buttons for zooming in and out, one direction at a time, or both. 4. You can make a specific point the center of the graphing window, click on the point, then the appropriate button on the tool bar. 5. Toggle between the regular and the tracing mode (F3 key or appropriate button on the tool bar), and explore tracing. 6. For a given function, you might use the tracing mode to find the coor- dinates of a point, the zeros, or extrema. 7. You can graph function, and you can graph the solutions of an equation in two unknowns. Try the hyperbola x 2 - y 2 = 1, or other equations of your choice. 8. You can graph in the cartesian plan (default), or you can use polar
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241lab - Lab Suggestions for Calculus I, Math 241/251...

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