Maple Tutor

Part 11: Practice Using Maple

Note: To receive help on a particular command, you can enter ? followed by the command word. At the end of the help screen you will find a set of examples that can be cut, pasted, and customized for your worksheet.

1. Calculate a decimal approximation to
   

2. The polynomial function P given by
   
   is a "good" approximation to the function y given by
   
   on some interval about the origin.
   (a) Compare the graphs of the two functions. Use the color and thickness options to enhance the comparison. Over what interval is P a good approximation to y?

   (b) Use the polynomial P to estimate the values of the integrals

   

   

   Compare your calculations with the values Maple produces for these integrals. (Note: you may find the evalf command handy.)

3. Let f be the function defined by
   
   (a) Use Maple to find the derivative of f. (Use the simplify command to clean up your answer.)

   (b) Graph f over the interval [-6, 6].

   (c) Create a plot of the graph of f together with a plot of the tangent line to the graph at x = 4. (Here you may want to use the subs command.)

   (d) From your plot in (c), estimate the number of times the tangent line crosses the graph.

   (e) Use the solve command to find the x-coordinates of the points of intersection of the graph and the tangent line.

   What is the difference between the solve and fsolve commands?

4. Use the animate command to create an animation of parabolas of the form y = cx², where c ranges from -10 to 10. Once you have created your frames, click on your graph, and experiment with the "VCR" button that appears at the top of the screen.
5.  
   (a) Plot a graph of the function f determined by
   
   How many inflection points does the graph appear to have?

   (b) Find the coordinates of these inflection points.

   (c) Create a plot showing the inflection points on the graph of f.

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modules at math.duke.edu

Copyright CCP and the author(s), 1998, 1999