Name(s) Lab 1--Maple Basics Click on the + button to expand a section and on the - button to close a section.

Dr. Behmard, Dr. Ward, Dr. Burton, Dr.Kruczek and the Maple built in Introduction. I have adjusted some of the contents for our specific course.

To learn how to use Maple software in order to enter, edit, and evaluate mathematical expressions, to graph functions, and to prepare properly formatted mathematical documents.

Carefully read all instructions and examples. Ask questions if you need any help. It is expected that everyone will actively participate in solving every problem. Hit Enter for every line of code that ends in a semicolon (;) or colon (:), even if there is no question. Note that Maple (somewhat annoyingly) jumps to the next line of code after you hit enter and you often have to scroll back up to where you were working. Answer every question (marked as Q:). If your answer is not obviously your answer, mark your answers with an A: Example: Q: What is your name? A: My name is Cheryl Beaver

BEFORE you start this lab, use the file menu and choose "File: Save As." RENAME 251 Lab 1.mws as LastnamesLab 1.mws. Use the last name of both you and your lab partner (if you have one). For example, is I was working alone my file name would be BeaverLab1.mws; if I was working with a lab partner named Sue Smith, our file name would be BeaverSmithLab1.mws. Save the file in your OWN DIRECTORY on your H: drive. While your are working SAVE YOUR WORK OFTEN (just hit Cntrl s).

This lab is due by Monday 10/6. LAB TURN IN: For Lab 1, email your completed lab to beaverc@wou.edu. Make sure you have properly named your file and reference "Math 251: Lab 1" in the subject line. TURN IN ONE LAB PER LAB TEAM.

Maple is a state-of-the-art mathematical problem solving system. It does all kinds of symbolic, graphical and numerical operations. Today we will just do some basic things which we will use through the quarter. (Some of them can be done just as well on a graphing calculator.) Save this sheet for reference. When you launch Maple, you automatically open a "worksheet" and you see a prompt like the following:

To input text into a Maple file you have three options: 1. Place the cursor in the desired position and click there. Then go to the Tool Bar (the bar right below all of the menu items) and click on the boldface T. 2. Choose "Insert Text" from the Insert menu. 3. Use the keyboard shortcut Ctrl T Text is used for explanatory notes like this, presented in black Times New Roman font by default. Use the Bold, Italic, Underline and paragraph formatting buttons in the tool bar just like you would with a word processor. All of these commands can also be found by choosing Character from the Format menu. This menu also allows you to change font type, size and color. You can also cut (Ctrl c), paste (Ctrl v) delete (Ctrl x), find (Ctrl f) and undo (Ctrl z) in Maple just like in a regular Word documents. You can cut and paste from Maple into Word as well. Since Maple does not have a spell check, you can cut and paste your whole Maple document into a Word document to check your spelling. You CANNOT just cut and paste the whole document back into Maple--Maple will just read the file as text and images if you do this and no longer work. Explore the drop down menus for features that you would like to use. Q0: You can practice entering text by entering your name and your lab partner's name in the space provided at the top of the lab, in the font and color of your choice.

One way to get help is to position the cursor anywhere in a command word (like plot) and then select the Help menu. The second item will read: Help on "plot" You can select that item. I find that looking at the examples provided at the end of a help topic often shows me what I want to know. I read the text only after checking the examples. A third way to get help to use the Topic Search or Full Text Search items in the Help menu. Both allow you to enter a key word. At the prompt below, get some help on plot. plot Close your help window by clicking the x in the upper right hand corner of the window. If you leave your help windows open you will reserve more memory for the actual worksheet you are working on and you will like run out of memory and experience some grief.

In order to enter a mathematical expression, place the cursor in the desired position and click there. Then go to the Tool Bar and click on the [> button (next to the text button T). After entering an expression, always finish the expression with a semi-colon (;) or a colon (:). Using a semi-colon tells Maple that you want to see the resulting output, and using a colon tells Maple that you do NOT want to see the output. For example, if you enter 3+5; (finished with a semi-colon), Maple will output an 8 in blue just below your expression (in red). If a colon is used, nothing will be printed on the screen, but Maple will remember whatever the command told it to remember. In order to evaluate a mathematical expression, place the cursor anywhere in the red text and hit enter. SYNTAX: The syntax for typing expressions in Maple is much like on a calculator except note the following (look carefully): (1) In all cases, multiplication must be typed explicitly, e.g. 2*cos(4) not 2 cos(4); (2) In all cases, the input to a function must be enclosed in parentheses, e.g. cos(4) not cos 4 and ln(2) not ln 2; For example, below is how one enters (32)(LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1JJW1zdXBHRiQ2JS1JI21uR0YkNiRRIzEyRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUY1NiRRIzEzRidGOC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnRjhGK0ZBRjg=) cos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnRjI= treating LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnRjI= as a variable. Note how LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnRjI= is handled. Place the cursor anywhere in the red text and then hit the Enter key to get the answer. 32*(12^13)*cos(pi); Q1: How is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnRjI= handled here? A1 For example, below is how one enters (32)(LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1JJW1zdXBHRiQ2JS1JI21uR0YkNiRRIzEyRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUY1NiRRIzEzRidGOC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnRjhGK0ZBRjg=) cos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnRjI= treating LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnRjI= as a value. Note how LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnRjI= is handled. Place the cursor anywhere in the red text and then hit the Enter key to get the answer. 32*(12^13)*cos(Pi); Q2: How is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnRjI= handled here? A2

The operations of addition, subtraction, multiplication, and division are represented by the symbols +, -, *, and /. To raise an expression to a power, we type ^ (shift 6). Now you can try. Determine the following (you have to type in the correct Maple expressions): Q3: Evaluate: 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 Q4: Evaluate: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1GIzYlLUkjbW5HRiQ2JFEjNTdGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnRjQtRiM2JS1GMTYkUSMyM0YnRjRGN0Y0LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZELyUpYmV2ZWxsZWRHUSZmYWxzZUYnRjdGNA== + LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1GIzYlLUkjbW5HRiQ2JFEjMTJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnRjQtRiM2JS1GMTYkUSMyM0YnRjRGN0Y0LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZELyUpYmV2ZWxsZWRHUSZmYWxzZUYnRjdGNA== If you press [Shift] [Enter] instead of just [Enter] at the end of an expression, then Maple sends you to a new line, but you stay within the same command line. This is handy if you need to enter a very long command (just hit [Shift] [Enter] without typing a colon or semi colon at any time to continue the command on the next line), or you want several things calculated all at once. For example: 3+5;..................................[Shift] [Enter] was used here instead of just [Enter] sqrt(25); Place your cursor on the above command line (in red, anywhere), and press [Enter], and you will see that Maple gives the answers to both expressions, in the same order. Also notice that sqrt is the Maple function for square root.

In this class we will be using trigonometric functions as well as natural logarithms and e, here are some Maple Commands for these functions. Just as in the example with the sqrt above, other functions evaluate expressions in a similar manner. For example, if you wanted to evaluate the sine function at 0, you would type sin(0); and hit Enter. Notice this gives you an exact answer Maple also provides an approximation in the form of a decimal value with the evalf command (which gives 10 decimal places by default). For example, evaluate the following: sin(2*Pi/3); evalf(sin(2*Pi/3)); Also: if you give Maple an expression that contains decimal places, Maple will carry out the calculation using decimals; usually an approximation of the true value. For example, evaluate the following: sqrt(0.5); sqrt(1/2); With the evalf command you can also specify how many decimal places you want your output to have. The default is 10 places, but if you wanted 50 or if you wanted 2, you would enter this in the expression as follows. For example, evaluate the following: evalf(sin(2*Pi/3),50); With the following examples, click on the expression to evaluate the expression pairs. Look for small differences in the expressions, and briefly explain what effect these small differences may have on the output. ln(1/2); ln(0.5); Q5: What effect does changing 1/2 to 0.5 have on the output?. A6:

You can easily include the previous decimal expansion in any subsequent calculation without having to re-type it. The % character refers to the last expression computed by Maple, in a manner analogous to the use of ditto marks when abbreviating words in English. For example, if you wanted to multiply a previous answer (for example LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSNsbkYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y3LyUmZmVuY2VHRjYvJSpzZXBhcmF0b3JHRjYvJSlzdHJldGNoeUdGNi8lKnN5bW1ldHJpY0dGNi8lKGxhcmdlb3BHRjYvJS5tb3ZhYmxlbGltaXRzR0Y2LyUnYWNjZW50R0Y2LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTi1JKG1mZW5jZWRHRiQ2JC1GIzYlLUkjbW5HRiQ2JFEiMkYnRjcvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnRjdGN0ZaRjdGK0ZaRjc=) by 2, and have 10 digits in the decimal approximation (or, second example, 2 digits), you would enter the following: ln(2); evalf(%*2); ln(2); evalf(%*2, 2); Using (%%) will give the second answer back, and so on. PLEASE NOTE: the previous answer is not necessarily the one right above the expression in which you are currently working, it is the LAST ANSWER THAT MAPLE CALCULATED. It could be at the end or beginning or anywhere in your worksheet. exp(1); ln(%); ln(e); Q6: What does exp do? Explain what is happening in this list of three values. A6: ln(%%); ln(exp(1)); ln(%%); Q7: Explain what is happening in this list of three values. A7: eval(exp(1)); eval(exp(1),50); evalf(exp(1)); evalf(exp(1),50); Q8: What does eval do? A8: Q9: What does evalf do? How is this different than eval? A9:

Here is how you assign a value to a VARIABLE: x:=6;......................................assigns 6 to x Note: The symbol ":=" means "is defined as." x+5;.........................................calculates x + 5 with x = 6 It may be necessary to clear a definition (if you don't want x = 6 anymore). You do this by "assigning x to x" like this: x:='x'; x+5;..................................................Notice the different result. Maple provides several ways to define FUNCTIONS. We will use the arrow mapping notation which closely resembles standard mathematical notation. Define the function 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. That is, the function which sends LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvRjNRJ25vcm1hbEYn to 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 which normally is written 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 . Notes: a. The "arrow" is typed as a minus sign followed by the greater than sign. b. The notation emphasizes that a function is a process that transforms an input via a rule into an output. After a function has been defined, Maple will evaluate it at any input we wish. Example: f := x -> x^2+1/2; You can evaluate the function at numeric and symbolic values. f(2);

f(a+b); If you delete the line which defines a function, the definition will no longer appear in the file, but Maple will still retain the definition in memory. For example, if you deleted the function above (highlight the line and press delete), and then typed in the expression f(2); you would still get LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1GIzYlLUkjbW5HRiQ2JFEiOUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRidGNC1GIzYlLUYxNiRRIjJGJ0Y0RjdGNC8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGRC8lKWJldmVsbGVkR1EmZmFsc2VGJ0Y3RjQ= as output. You can clear a function definition in the same way you clear a variable definition (by giving Maple the command f : = ' f ' ; ). Maple maintains the last definition you send to Maple (not necessarily the definition closest definition to where the cursor is). Some more practice: The following command defines the squaring function, which we will name "s". s := x -> x^2; For instance, we can evaluate the function s above at input -3 by simply typing: s(-3); The answer should be 9. Q10: Explain this A10: Additionally, we can change the function s above at input -3 by simply typing, for example: -s(-3); The answer should be -9. Q11: Explain this A11: Q12: Assign the value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSVzaXplR1EjMTJGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRidGMg== to the variable z. Then define g(w) to be LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2I1EhRictRiM2LEYrLUYjNictSSVtc3VwR0YkNiUtRiw2JVEid0YnLyUlYm9sZEdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW5HRiQ2JlEiMkYnRjkvJSdpdGFsaWNHRjsvRj1RJ25vcm1hbEYnLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0Y5RkMvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnRkUtSSNtb0dGJDYvUSIrRidGOUZDRkUvJSZmZW5jZUdGOy8lKnNlcGFyYXRvckdGOy8lKXN0cmV0Y2h5R0Y7LyUqc3ltbWV0cmljR0Y7LyUobGFyZ2VvcEdGOy8lLm1vdmFibGVsaW1pdHNHRjsvJSdhY2NlbnRHRjsvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0Zbby1GIzYpLUZANiZRIjNGJ0Y5RkNGRS1GTjYtUTEmSW52aXNpYmxlVGltZXM7RidGRUZRRlNGVUZXRllGZW5GZ24vRmpuUSYwLjBlbUYnL0Zdb0Znb0Y2RjlGQ0ZKRkUtRk42L1EoJm1pbnVzO0YnRjlGQ0ZFRlFGU0ZVRldGWUZlbkZnbkZpbkZcby1GQDYmUSI0RidGOUZDRkVGOUZDRkpGRUYrRjlGQ0ZKRkU= . Calculate g(4), 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 and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1GIzYnLUkjbWlHRiQ2I1EhRictRiM2KUYwLUYjNictRjE2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y/USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGSS8lKXN0cmV0Y2h5R0ZJLyUqc3ltbWV0cmljR0ZJLyUobGFyZ2VvcEdGSS8lLm1vdmFibGVsaW1pdHNHRkkvJSdhY2NlbnRHRkkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZYLUkobWZlbmNlZEdGJDYkLUYjNidGMC1GIzYnLUYxNiVRInhGJ0Y7Rj4tRkI2LVEiK0YnRkVGR0ZKRkxGTkZQRlJGVC9GV1EsMC4yMjIyMjIyZW1GJy9GWkZjby1GMTYlUSJoRidGO0Y+LyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJ0ZFRjBGaG9GRUZFRmhvRkUtRkI2LVEoJm1pbnVzO0YnRkVGR0ZKRkxGTkZQRlJGVEZib0Zkby1GIzYnRjhGQS1GZm42JC1GIzYlRlxvRmhvRkVGRUZob0ZFRjBGaG9GRUYwRmhvRkUtRiM2JUZlb0Zob0ZFLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZbcS8lKWJldmVsbGVkR0ZJRmhvRkU=. (Note: To convert the preceding fraction into a math format while writing text, we (1) type (g(x+h)-g(x))/h, (2) highlight the equation, (3) Click on Format (4) Then Convert To (5) Then Standard Math. A12:

Maple's two-dimensional plotting tools allow you to graph multiple functions and modify the range and axes as you desire. You also have full control over the fonts used for titles, labels, and other text in your plots. To begin graphing, one (usually) must type the following command once. It tells Maple to load some packages needed for graphing. Enter it now with(plots); (You should get a long blue list of all the different plotting commands. Compare this to typing a colon. with(plots): The following generates the plot of 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 Place the cursor anywhere in the red text and hit enter to see the graph Note, we must clear x first because we used it earlier. x:='x'; plot(tan(x), x); This can be read "plot tangent of x with respect to x TIP FOR GRAPHING: Click on a graph and look in the upper left hand corner to see the coordinates of the point that you have clicked on. Notice this is often only an approximation of the point you are looking at. For example, if the point is (1/3, 2/3) you'll probably see (.32, .68). If you want to change the range (the ugly plot above suggests that we do want to) in order to view the plot differently, this is possible by assigning ranges to x and y as follows (you just type two periods for the range "dots"): The ranges are the intervals for the x values and the y values--just like with your calculator. plot(tan(x), x=-5..5, y=-10..10); I you want to edit the graph's attributes after it is displayed, click anywhere on the graph and notice that the menu items at the top of the screen change. You can use these menu items to change thickness of the lines or style of the axes, etc. or you can click on the graph with the RIGHT mouse button, and a quick pull down menu appears with the same choices as above. You may want to plot more than one function at once, use curly brackets and separate the functions to be plotted with commas: plot({sin(x), cos(x)}, x); Compare this to defining the x and y ranges plot({sin(x), cos(x)}, x=-2..2, y=-2..2); Or you may want to plot a set of ordered pairs: plot([[5,5],[6,6],[7,8],[9,20]]); Q13 and Q14 Define any function (like 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) and plot the function. Practice using the graphics tools to edit the output. Show two different graphs and note what features you have changed or enhanced after the graph. A13 A14

Q15: (a) Recall that a power function is a function of the form f(x)=xa where a is a positive integer. For all of the following (b) - (d); Let x range from input -2 to input 2. For all of the following make all three graphs show in black. Check plot help to find out how to choose the color of the graph. A15(a) Summary Comments: (b) Graph on the same set of axes any three power functions with a an even positive integer. Summarize what appears to be the general shape of this type of power functions. A15(b) Summary Comments: (c) Graph on the same set of axes any three power functions with a an odd positive integer. Summarize what appears to be the general shape of this type of power functions. A17c Summary Comments: (e) The next natural questions is to graph on the same set of axes any three power functions with a=1/n and n an ODD positive integer. However, Maple, like graphing calculators are limited by their computational procedures. What is the domain of 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? Graph 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 with x = -2..2 AND with y = -2..2 and you will see that Maple does not graph 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 correctly. This is an error in Maple, not in your understanding of the domain of the cube root function. We will be sure to be careful with this detail as the term proceeds. Graph 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here: A15(e) Summary Comments:

Check your work carefully, make sure you answered all of the questions and that all of your answers are clearly marked. Make sure you have two saved copies (your directory, your disc) and that your file is named Yourlastname Lab1.mws. Email your lab to me at beaverc@wou.edu and email a copy to your lab partner if you have one. Remember you should only turn in one lab per lab team.