Casio CLASSWIZ CG Software User's Manual page 112

*3 Drawing is possible when u
Convergence or Divergence of a Numeric Sequence" (page
*4 Drawing is possible when u
From Two Sequences" (page
*5 See "Specifying the Display Range of the Graph Window (View Window)" (page
Drawing a Phase Graph From Two Sequences
You can create numeric tables (sequences) from two recursion formulas and then draw a Phase Graph using
the values of one formula as the horizontal axis and the values of the other formula as the vertical axis.
Example: To input the two two-term recursion formulas u
terms are u
1
n from 1 to 10, and then use the sequences to draw a Phase Graph.
1. On the Sequence tab, press u to highlight the first line.
2. Press O, and then use the Setup menu that appears to configure the settings shown below.
• [Type] > [u ]
n+1
• [First Term] > [ u ]
1
• [Set Table Domain] > [Start]： 1 ; [End]： 10
3. On the Sequence tab, input u
4. Press > to go to the Table tab.
5. Select T > [Phase Graph].
6. On the View Window menu that appears, input the values shown below.
x Minimum = 0, x Maximum = 2, x Scale = 1
y Minimum = 0, y Maximum = 4, y Scale = 1
and then press O.
7. Highlight
• Phase Graph appears on the Table tab.
Note
• A Phase Graph can be drawn when u
• The x -axis values are those of the formula that is higher in the Sequence tab list, while the y -axis
values are those of the lower formula.
• The color used to draw the graph is the color assigned to the formula that is higher in the Sequence
tab list.
• If three regression formulas ( u
creation, a menu will appear in step 5 above asking you to select two of the three ( u
• If S > [ Σ Display] is turned on, a menu will appear to select whether to graph using u
Σu (cumulative sum of sequences) in step 5 above.
n
Using Web Graph to Check the Convergence or Divergence of a Numeric Sequence
For example, graph y = f (x) where u
in terms of u and u . Overlap this with a straight line with a slope of 45 degrees (graph of y = x). You can
n + 1 n
use these two graphs to draw a web graph automatically.
Selecting [Web Graph] in the example procedure below automatically graphs y = f (x) and draws a straight line
with a 45-degree slope. Then you can simply press O multiple times to draw the web graph. By observing the
behavior of the web graph, you can intuitively grasp whether the sequence is convergent or divergent.
is selected as the formula type. See
n+1
, u , or u is selected as the formula type. See
n n+1 n+2
112).
= 1 and v = 1 respectively. Next, create sequences that change the value of variable
1
= 0.9u , u
n + 1 n 1
, u
n n+1
, v , w ) have been entered and all three are selected for numeric table
n n n
= y and u
n + 1
112).
= 0.9u and v
n + 1 n
= 1, v + 0.1n − 0.2, v
= v
n + 1 n
, or u is selected as the formula type.
n+2
= x in a two-term recursion formula that can be expressed
n
112
"Using Web Graph to Check the
"Drawing a Phase Graph
80).
= v + 0.1n − 0.2, where the first
n + 1 n
= 1.
1
- v , v - w
n n n
(sequence) or
n
, u - w ).
n n n