Math 150, Maple Assignment # 1

Note: This lab is due in class by Wednesday/Thursday 17/18 October

Objectives: 1. Getting acquainted with Maple. 2. Be able to use Maple to do manipulations with functions. 3. Be able to plot functions in Maple.

Lab Procedure: You will work on the lab preferably with a partner (and turn in one written lab for the two of you). When you are done, complete all of the following steps:

1. Clean up your file -- Edit out work that doesn't lead to a solution. -- Did you respond to all prompts/ questions accurately and thoroughly? 2. Put your name(s) at the top of the file. 3. Save the file, and send your partner a copy (if necessary). 4. Print out a copy and turn it in class by the above due date.

Working in Maple A note about Maple help: If you have questions about how to get Maple to do a particular action or a question on command syntax, the program has an extensive collection of helpfiles which are located in the menu above as Help > Maple Help.

After opening the Maple icon, go to File > New > Worksheet Mode. This will open up a worksheet on which you can do your math work. (Note the cursor >).

When starting a new problem, it is helpful to clear the definitions of previously used variables so that they may be used in a new context. To clear all Maple definitions, use > restart;

When defining variables and functions, use the ":=" notation instead of just "=". Maple understands the colon-equals combination as a definition, and the use of only the equal sign as an equation.

Example: Here's how to define the function f(x) = x^2 in Maple: > f := x -> x^2;

Note the unusual notation to define a function f. The “:=” initializes the function f, while the “x->x^2” says that for an input x, we get output x^2. (Beware of the cursor; sometimes after using the ^ for powers, you need to press the space bar to get out of the exponent! Also, every Maple command must end with a semicolon!

With this, you can do all sorts of things: > f (2); (you should get 4; note the semicolon in Maple)

> (f (x+h) - f(x)) /h; (this should display in a nicer form what you just typed)

> expand(%); (The % sign recalls the expression from the previous line, while “expand” algebraically simplifies the expression.)

> subs(x = 2, f(x)); (This will substitute x = 2 into f(x).)

There are other nice things you can do, too. In the side bar, you should see the “expression” section. By clicking on the derivative icon, you can have Maple do the derivative work for you! (See additional attached page for details.)

Using these icons, you can do many things without remembering the Maple code to do them!

Lab Homework 1. Using Maple, define g(x) = x^3/(x+3) [use the right cursor and parentheses as necessary]. Use this to find g(2), g(x+h) –g(x), and even (g(x+h) – g(x))/h.

2. Use the derivative command to evaluate g’(x). Double check it manually with the quotient rule. What type of algebra is Maple doing to make its answer look different from yours?

3. Compute lim(x0) 1/(sqrt(x+4) – 2) using Maple. Do you believe this? Use the plot command as follows to see graphical evidence.

> h(x) := 1/(sqrt(x+4) – 2); > plot(h(x), x = -2 .. 2); > >