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Texas Instruments TI-89 Guide

Texas Instruments TI-89
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TI-89 Guide
TI89-25
Copyright © Houghton Mifflin Company. All rights reserved.
We estimated the limit as x gets very large or very small to be
0.273. Now, u(0) = 0, and it does appears from the graph that u
is never negative. Set a window with values such as
xmin =
10,
xmax = 10, ymin = 0,
and
ymax = 0.35.
Press
F3 (GRAPH).
To examine the limit as x gets larger and larger, change the win-
dow so that
xmax = 100,
view the graph with
F3 (GRAPH),
change the window so that
xmax = 1000,
view the graph with
F3 (GRAPH),
and so forth. The graph to the right was drawn
with
xmax = 10,000
.Use
F3 [Trace]
with each graph.
Repeat the process as x gets smaller and smaller, but change
xmin
rather than
xmax
after drawing each graph. The graph to the right
was drawn with
xmin =
9000, xmax = 10, ymin = 0,
and
ymax =
0.35.
Again, press
F3 [Trace]
on each graph screen to view some
of the outputs and confirm the numerical estimates.
1.4.5 FI NDI NG LI MI TS ALGEBRAI CALLY As previously mentioned, the TI-89 finds limits
algebraically. You can use this feature to confirm numerical and graphical estimates or use it as
a method of finding limits. The TI-89 syntax is
limit (function, input variable, point, direction).
For a limit from the left,
direction = any negative number
; for a limit from the right,
direction =
any positive number
; for a limit from both sides,
direction = 0
or
direction
is omitted from the
instruction. We illustrate using the function u that appears in Example 2 of Section 1.4.
Press
HOME F4 1[Define]
and type
u(x)=
33
9112
2
2
xx
xx
+
++
.Find
lim
x
1
u(x).
Access the limit instruction with
F3
[Calc] 3 [limit(].
NOTE: We used
3 to indicate the direction in the limit statement. The TI-89 considers only
thenegativesign,soanynegativenumbergivesthesameresulttryit! Alsorememberthatif
you want a decimal approximation for the answer,
ENTER
gives it.
Find
lim
x
1
+
u(x),
lim
x
1
u(x),
lim
x
2/9
u(x),
lim
x
2/9
+
u(x), and
lim
x
2/9
u(x).
(See the note below for a shortcut.)
NOTE: Instead of retyping the limit statement each time to find the above limits, remember
that when the entry line is highlighted, you can press
to put the cursor on the right-hand
side of the statement and press
to put the cursor on the left-hand side of the statement. The
statement is ready for editing using the arrow keys to move to the correct location and using
to delete unwanted symbols.

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Texas Instruments TI-89 Specifications

General IconGeneral
Display size (HxV)100 x 160 mm
Memory type639K FLASH ROM, 188K bytes RAM
Compatible operating systemsOperating System 2.09
Battery typeAAA

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