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I WEB Graph (Convergence, Divergence)
y = f(x) is graphed by presuming a
n
+1
= y, a
n
= x for linear two-term regression a
n
+1
= f(a
n
)
composed of a
n
+1
, a
n
. 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 U several 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
a
n
+1
= –3(a
n
)
2
+ 3a
n
, b
n
+1
= 3b
n
+ 0.2, and check for divergence or convergence. Use the following
table range: Start = 0, End = 6, a
0
= 0.01, a
n
Str = 0.01, b
0
= 0.11, b
n
Str
= 0.11
K RECUR
(V-WIN)?U@U@UA
?U@U@U)
(TYPE)(
a
n
+1
)B(a
n
)VB(a
n
)U
B(b
n
)?AU
(SET)(a
0
)
?UEU??@U?@@UA
??@U?@@U)
(TABL)
(WEB)
U~U(a
n
is convergence)
AU~U(b
n
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.