Go through the following exercises. Your report should be in the form of a Maple worksheet, showing your work. Be warned that some of the commands given below do not work correctly. If you find one that generates an error or a wrong answer, explain the error in your worksheet.

- At the Maple prompt, enter the polynomial expression
p:=1/4*x^3 - 1/5*x^2 -3*x -1;

- Enter the following four Maple commands. For your report,
describe what you get. Why does Maple distinguish between
**2**and and and ?subs(x=2,p); subs(x=2.0,p); subs(x=1/2,p); subs(x=.5,p);

- Maple can also substitute expressions into other expressions.
The next group of commands lead you through a derivation of the
derivative of the expression
**p**, which we'll learn about this term. For your report, explain what Maple is doing in each step, except the one involving`limit`, where you can speculate if you wish.a1:=subs(x=a,p); a2:=subs(x=a+h,p); a3:=(a2-a1)/h; a3; a4:=simplify(a3); a5:=limit(a4,h=0);

- In the tutorial, you set the
**x**range for the`plot`command. You can also set the**y**range for a plot, as shown in the second command below. Can you think of a reason you would want to set the**y**range?plot(p,x=-5..5); plot(p,x=-5..5,y=-5..5);

- Enter the following four Maple commands. For your report,
describe what you get. Why does Maple distinguish between
- Repeat the first problem, but using a function instead of an
expression. First, enter the following function definition.
f:= x -> x^3/5 -x^4/4 -2*x -1 end;

The Maple commands using are given below to help you. Note any differences between how Maple handles functions and expressions.

f(t); f(2); f(2.0); f(1/2): f(.5); b1:=f(a); b2:=f(a+h); b3:=(b1-b2)/h; b3; b4:=simplify(b3); b5:=limit(b4,h=0); plot(f(t),t=-5..5); plot(f(t),t=-5..5,s=-5..5);

- Occasionally you have to investigate functions that are defined
piece-wise. In this task, and the
next, use defined by
This is entered in Maple by

f:=t -> if t < 2 then t^2 else t fi;

Then try each of the following commands.

f(-1); f(3); f(1/2); f(b); plot(f,t=-2..4); plot(f(t),t=-2..4); plot('f(t)',t=-1..5); plot('f(t)',t=-1..5,style=LINE);

Remember to close all the plot windows when you are done looking at the graphs.

- Use the instructions in the handout to print a plot of the
function used in the previous exercise. Include the plot with your lab
writeup. If you are feeling adventurous, paste the plot right into
your Maple worksheet.
- Maple makes a strong distinction between an expression and a
function. In your own words, describe how these two
**mathematical**concepts differ. Note the word**mathematical**in the previous sentence. You are not being asked to simply describe how Maple handles expressions and functions, but to explain the concepts.

Mon Jun 26 13:37:30 EDT 1995