MATH 202 |
SPRING 2002 |

on Graphing Calculators

Here are some examples showing how to graph the partial sums of a power series the TI-83 Plus, the TI-85, and the TI-89. We will plot the 3^{rd}, 6^{th}, 9^{th}, and 12^{th}partial sums of the power series

As you can check, the interval of convergence for this series is [-1, 5). We'll have our plotting window go from

x=-2tox=6, so that we can see what happens when we reach the ends of the interval of convergence.Click on the appropriate link to jump to the example using the TI-83 Plus, the TI-85, or the TI-89.

sum(seq((X-2)^N/(N*3^N),N,1,3,1))To get the symbol

sum(, we press[2nd][LIST]then right-arrow twice to highlightMATH, then[5]to selectsum(. To get the symbolseq(, we press[2nd][LIST]then right-arrow once to highlightOPS, then[5]to selectseq(. We enter the rest of the formula using the ordinary numeric and alphabetic keys. (The variableNis keyed in using[ALPHA][N].)Here's what the

Y=screen looks like when we finish.

Next we press

[WINDOW]to bring up theWINDOWscreen. We'll setXminto-2,Xmaxto6, andXsclto1. ForYminandYmax, we'll have to take a guess, because we don't know what the range of this power series might be. We do know it has to cross thex-axis (atx=2), so we'll chooseYminto be negative andYmaxto be positive. We start with-2and2.Here's the

WINDOWscreen with our initial settings.

Next we press

[GRAPH]and wait while the calculator draws a graph of the third partial sum of our series.

To add the 6

^{th}, 9^{th}, and 12^{th}partial sums, we need only enter them on theY=page. Here's an easy way to do that:

1. We use the arrow keys to move the cursor to the point after Yon the_{2}=Y=page.2. We type [2nd][RCL]. The symbolRclappears at the bottom of the screen.3. We type [VARS]to bring up theVARSscreen, then use the right-arrow key to highlightY-VARS. We press[ENTER]to selectFunctionand then[ENTER]again to selectY._{1}4. This puts us back on the Y=screen, with the symbolRcl Yat the bottom of the screen. We press_{1}[ENTER]once again. The formula forYmagically appears as the definition of_{1}Y_{2}5. We use the arrow keys and the [DEL]and[2nd][INS]keys as necessary to change the3in the definition ofYto a_{2}6.6. We use the arrow keys to move the cursor to the point after Y, and repeat steps 2 through 5, this time changing the_{3}=3to a9.7. We use the arrow keys to move the cursor to the point after Y, and repeat steps 2 through 5, this time changing the_{4}=3to a12.Once we've defined all four functions, we press

[GRAPH]again and watch patiently while the calculator draws all four curves.

A useful tip:While the calculator is graphing a function, it won't respond to any keyboard input. If the drawing takes too long, you can interrupt it (and regain control of the calculator) by pressing the[ON]key.

, we pressOn the TI-85[2nd][MODE]to verify that the calculator is in the proper mode. We use the arrow keys to highlightFuncas a plotting mode. We then press[GRAPH][MORE]and[F5]to bring up the graphing format page, where we make sure thatDrawLineis highlighted.sum seq((x-2)^N/(N*3^N),N,1,3,1)We find

sumandseqby pressing[2nd][LIST][F5][MORE], and use these along with the usual alphanumeric keys to enter the formula.Here's what the

y(x)=screen looks like when we finish.

Next we press

[GRAPH]again and then[F2]to bring up theRANGEscreen. We'll setxMinto-2,xMaxto6, andxSclto1. ForyMinandyMax, we'll have to take a guess, because we don't know what the range of this power series might be. We do know it has to cross thex-axis (atx=2), so we'll chooseyMinto be negative andyMaxto be positive. We start with-2and2.Here's the

RANGEscreen with our initial settings.

Next we press

[F5](to selectGRAPHand wait while the calculator draws a graph of the third partial sum of our series.

To add the 6

^{th}, 9^{th}, and 12^{th}partial sums, we need only enter them on they(x)=page. Here's an easy way to do that:

1. We press the down-arrow key to bring up the y2=cursor.2. We type [2nd][RCL]. The symbolRclappears at the bottom of the screen.3. We type [F2]to selectyand then[ALPHA](to cancel alphabetic mode) and[1]. The bottom of the screen now saysRcl y1. We press[ENTER]. They1formula now appears aftery2=.4. We use the right- and left-arrow keys, along with [2nd][INS]and[DEL](as necessary) to change the3in the formula fory2to a6. (Some of the formula will be scrolled off the edge of the screen; use the arrow keys to get there.)5. We press the down-arrow key to bring up the y3=prompt, and repeat steps 2 through 4, this time changing the3to a9.6. We use the down-arrow keys to bring up the y4=and repeat steps 2 through 4, this time changing the3to a12.Once we've defined all four functions, we press

[GRAPH][F5](to select theGRAPHoption), and watch patiently while the calculator draws all four curves.

A useful tip:While the calculator is graphing a function, it won't respond to any keyboard input. If the drawing takes too long, you can interrupt it (and regain control of the calculator) by pressing the[ON]key.

, We first make sure the calculator is in the proper mode. We pressOn the TI-89[MODE], and if theGraphmode is notFUNCTION, we use the arrow keys to change it toFUNCTION. We press[ENTER]to record our changes.To do this, we start from the home screen, and press

[F4]and[ENTER]to bring up the wordDefinein the formula entry line. We use the alphanumeric keys to enter the formula

(The summation sign is on the

Calcmenu, which we get to by pressing the[F3]key.)We finish the formula by pressing

[ENTER]. Here is what the home screen looks like.

Next we press

[(diamond)][F1]to go to theY=screen. (The symbol "(diamond)" is the green diamond key, just under the[2nd]key.) On theY=page, we use the alphanumeric keys to sety1tos(3,x),y2tos(6,x)y3tos(9,x), andy4tos(12,x).Here's what the

Y=screen looks like when we're finished.

Next we press

[(diamond)][F2]to bring up theWINDOWscreen. As discussed above, we want to plot these sums for values ofxbetween -2 and 6. We have to guess at the values foryminandymax. We do know that all the partial sums cross thex-axis (atx=2), so we start withymin=-2andymax=2.We set

xsclandysclto1, and either leavexresalone or set it to1as well.(When

xresis 1, the calculator evaluates the function at every pixel. This provides for a more accurate graph, but slows down the plotting. Whenxresis 2, the calculator evaluates the function at every other pixel.)

We press

[(diamond)][F3]to draw the picture. It looks like this:

A useful tip:While the calculator is graphing a function, it won't respond to any keyboard input. If the drawing takes too long, you can interrupt it (and regain control of the calculator) by pressing the[ON]key.