Calculator User Manual

254
Chapter 19: Applications
19APPS.DOC TI-86, Chap 19, US English Bob Fedorisko Revised: 02/13/01 2:41 PM Printed: 02/13/01 3:05 PM Page 254 of 1819APPS.DOC TI-86, Chap 19, US English Bob Fedorisko Revised: 02/13/01 2:41 PM Printed: 02/13/01 3:05 PM Page 254 of 18
쐈
Support this conjecture by graphing
y1
,
y2
(to which Cp(x) is
stored), and
Plot1
together.
쐉
In the equation editor, enter the apparent characteristic
polynomial of matrix
A
and select ¼ (thick) graph style as shown.
¼y3=
L
x^3+14x
N
24
씈
Graph
y1
,
y2
,
y3
, and
Plot1
.
씉
Deselect
y2
in the equation editor.
씊
Select
TABLE
from the
TABLE
menu to display
y1
and
y3
in the
table.
Compare the values for the characteristic polynomial.
Convergence of the Power Series
A closed-form analytic antiderivative of (sin x)
à
x does not exist. However, substituting t for
x, you can find an infinite series analytic solution by taking the series definition of sin t,
dividing each term of the series by t, and then integrating term by term to yield:
ˆ
G
L
1
n+1
t
2n
N
1
à
((2n
N
1)(2n
N
1)!)
n=1
Plot finite approximations of this power series solution on the TI
-
86 with
sum
and
seq
.