Math 331
Exercise 1: Some elementary Maple

Due Wednesday, September 18

This exercise is just to demonstrate that you have paid enough attention to do some simple calculations in maple. Since maple will be our primary tool in this class, its rather important that you be able to interact with it.

Use maple to solve the following problems. Hand in a printout of your maple worksheet.

1.

Evaluate to 30 decimal places.

2.

Consider the function

a.

Write this in a simpler form (ie, factor and reduce it).

b.

Draw a graph of the function for . Adjust the vertical range so that some of the detail can be seen.

c.

Compute the area under the curve between 0 and 4 (i.e. integrate the function). Give your answer both in an exact form and as a decimal approximation to about 10 places.

d.

What is the value of the integral if you remove the factor of ?

3. What is the sum of the cubes of the first 50 integers? That is, compute

What are its integer factors?

4. Find the solutions to the system of equations

5. Draw a graph showing both cos(x) and its fifth taylor polynomial (that is, ) for x between -4 and 4. How many terms do you seem to need to get ``good agreement'' in this range (you will need to use something like

to make this work. see the help for more details).