IWEB Graph (Convergence, Divergence)

y = f(x) is graphed by presuming an+1 = y, an = x for linear two-term regression an+1 = f(an) composed of an+1, an. Next, it can be determined whether the function is convergent or divergent.

1.From the Main Menu, enter the RECUR mode.

2.Make V-Window settings.

3.Select 2-term recursion as the recursion formula type, and input the formula.

4.Specify the table range, n start and end points, initial term value, and pointer start point.

5.Display the recursion formula number table.

6.Draw the graph.

7.Press U, and the pointer appears at the start point you specified. Press Useveral times.

If convergence exists, lines that resemble a spider web are drawn on the display. Failure of the web lines to appear indicates either divergence or that the graph is outside the boundaries of the display screen. When this happens, change to larger V-Window values and try again.

You can use DA to select the graph.

Example

To draw the WEB graph for the recursion formula an+1 = –3(an)2+ 3an, bn+1

 

= 3bn + 0.2, and check for divergence or convergence. Use the following

 

table range: Start = 0, End = 6, a0 = 0.01, anStr = 0.01, b0 = 0.11, bnStr

 

= 0.11

KRECUR

(V-WIN)?U@U@UA ?U@U@U)

(TYPE)(an+1) B(an)VB(an)U B(bn)?AU

(SET)(a0)

?UEU??@U?@@UA ??@U?@@U)

(TABL)

(WEB)

U~U(an is convergence)

AU~U(bn is divergence)

•To change the graph line style, press (SEL+S) after step 4.

•With WEB Graph, you can specify the line type for a y = f(x) graph. The line type setting is valid only when “Connect” is selected for “Draw Type” on the Setup screen.

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