User Manual

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Recursion Table and

Graph

You can input two formulas for any of the three following types of

recursion, which you can then use to generate a table and draw

graphs.

•General term of sequence {an}, made up of an and n

• Formulas for linear recursion between two terms, made up of

an+1, an, and n

• Formulas for linear recursion between three terms, made up of

an+2, an+1, an, and n

16-1 Before Using the Recursion Table and Graph Function

16-2 Inputting a Recursion Formula and Generating a Table

16-3 Editing Tables and Drawing Graphs

Chapter

Summary of content (12 pages)

PAGE 1
Chapter 16 Recursion Table and Graph You can input two formulas for any of the three following types of recursion, which you can then use to generate a table and draw graphs.
PAGE 2
16-1 Before Using the Recursion Table and Graph Function uTo enter the RECUR Mode On the Main Menu, select the RECUR icon and enter the RECUR Mode. This causes the Recursion Menu to appear. Selected storage area Press f and c to move. • All recursion formulas that are stored in memory appear in the Recursion Menu. CFX fx-9750G PLUS • {SEL+C} ... {menus for control of table generation and graph color} • {SEL} ... {recursion formula generation/non-generation status} • {DEL} ...
PAGE 3
16-2 Inputting a Recursion Formula and Generating a Table Example 1 To input an+1 = 2an + 1 and generate a table of values as the value of n change from 1 to 6 Make a1 = 1. 1. Specify the recursion formula type as linear recursion between two terms and then input the formula. c4(n, an···) 2(an) +b 2. Press w5 (RANG) to display the table range setting screen, which contains the following items. • {a0}/{a1} ... setting of value for {a0(b0)}/{a1(b1)} P.
PAGE 4
16 - 2 Inputting a Recursion Formula and Generating a Table • Displayed cell values show positive integers up to six digits, and negative integers up to five digits (one digit used for negative sign). Exponential display can use up to three significant digits. • You can see the entire value assigned to a cell by using the cursor keys to move the highlighting to the cell whose value you want to view. P.7 • You can also display the sums of the terms (Σan or Σbn) by turning on Σ Display.
PAGE 5
Inputting a Recursion Formula and Generating a Table 16 - 2 4. Display the table of the recursion formula. At this time, a menu of table functions appears at the bottom of the screen. J6(TABL) Currently selected cell (up to six digits) Value in currently highlighted cell • There can be only one recursion table stored in memory at one time.
PAGE 6
16 - 2 Inputting a Recursion Formula and Generating a Table uTo specify the generation/non-generation status of a formula Example To specify generation of a table for recursion formula an+1 = 2an + 1 while there are two formulas stored c 1(SEL+C) 1(SEL) ... 1(SEL) J (Selects recursion formula to which non-generation status is to be assigned and then specifies nongeneration status.) Unhighlights this formula 6(TABL) (Generates table.
PAGE 7
16-3 Editing Tables and Drawing Graphs You get a choice of four options for editing tables and drawing graphs. • Deletion of a recursion formula table • Drawing of a connect type graph • Drawing of a plot type graph • Drawing of a graph and analysis of convergence/divergence (WEB) You can access these options from the function menu that appears at the bottom of the screen whenever a table is displayed. • {FORM} ... {returns to Recursion Menu} • {DEL} ... {table delete} P.225 • {WEB} ...
PAGE 8
16 - 3 Editing Tables and Drawing Graphs uTo specify the color of the graph ({BLUE}/{ORNG}/{GRN}) CFX The default color for a graph is blue. Use the following procedure to change the graph color to orange or green. 1. Display the Recursion Menu and then use f and c to highlight the formula whose graph color you want to change. 2. Press 1 (SEL+C). 3. Press the function key that corresponds to the color you want to specify.
PAGE 9
Editing Tables and Drawing Graphs Example 2 16 - 3 Draw a graph of an+1 = 2an + 1 with Σan on the vertical axis and n on the horizontal axis, and with the points unconnected. Use the same View Window parameters as those provided in Example 1. 6(TABL)6(G·PLT) (Selects plot type.) 6(Σan) (Draws graph with Σan on the vertical axis.) • To input a different recursion formula after a graph is drawn, press ! Q. This displays the Recursion Menu where you can input a new formula.
PAGE 10
16 - 3 Editing Tables and Drawing Graphs 2. Press w, and the pointer appears at the pointer start point (anStr = 0.01). • The Y value for the pointer start point is always 0. 3. Each press of w draws web-like lines on the display. w w ↓ ↓ This graph indicates that recursion formula an+1 = –3an2 + 3an is convergent. Example 2 To determine whether or not the recursion formula bn+1 = 3bn + 0.2 is convergent or divergent. Use the following table range. Start = 0 End b0 bn Str = 0.02 = 0.
PAGE 11
Editing Tables and Drawing Graphs 16 - 3 2. Press w and then either f or c to make the pointer appear at the pointer start point (bnStr = 0.02). • The Y value for the pointer start point is always 0. 3. Each press of w draws web-like lines on the display. w w ↓ ↓ This graph indicates that recursion formula bn+1 = 3bn + 0.2 is divergent. • Inputting bn or n for the expression an+1, or Inputting an or n for the expression bn+1 for linear recursion between two terms causes an error.
PAGE 12
16 - 3 Editing Tables and Drawing Graphs k Drawing a Recursion Formula Graph Using Dual Screen P.7 P.224 Selecting “T+G” for the Dual Screen item of the set up screen makes it possible to display both the graph and its numerical table of values. Example To draw the graph of an+1 = 2an + 1 from Example 1, displaying both the graph and its table Display the set up screen and specify “T+G” for Dual Screen. Press J. 6(TABL) (Shows the table.) 6(G·PLT) (Draws plot type graph.