Texas Instruments TI-89 Manual page 22

TI 89-22
value to one more decimal place (here, to 4 decimal places) for three consecutive outputs. Then, round
that common value off to the requested 3 places for the desired limit. Your instructor may establish a
different rule from this one, so be sure to ask.
Using this Rule of Thumb and the results that are shown on the last calculator screen, we estimate that
lim
u(x) = 0.429. We now need to estimate the limit from the right of
−
−
x→ 1
Delete the values currently in the table
lim
u(x), enter values to the right of, and becoming closer and
+
−
x→ 1
−
closer to, 1. (Note: Again, the values that you enter do not
have to be those shown in the text or these shown to the right.)
Because the output 0.4285... appears three times in a row, we estimate that
0.429. Then, because
We now illustrate finding the limit in part b of Example 2 in Section 1.4 of Calculus Concepts:
Delete the values currently in the table
lim
u(x), enter values to the left of, and becoming closer and
−
−
x→ 2/9
−
closer to, 2/9 =
to become larger and larger, we estimate that
Delete the values currently in the table
lim
u(x), enter values to the right of, and becoming closer
+
−
x→ 2/9
−
and closer to,
larger and larger, we estimate that
lim
u(x) does not exist.
−
x→ 2/9
1.4.2 CONFI RMI NG LI MI TS GRAPHI CALLY – ZOOMI NG I N AND OUT
be used to confirm a limit that you estimated numerically. You also can zoom in or zoom out
on the graph to obtain a better view of the limit you are estimating. We again illustrate using
the function u that appears in Example 2 of Section 1.4 in Calculus Concepts.
Have the function u(x) =
of the list. A graph drawn with
Y=
F2 [Zoom] 6 [ZoomStd]
To confirm that
values of u that are near
for the x-view and evaluate the function at those x-values to help
determine the y-view. We manually set the window to values
such as those shown to the right and draw the graph.
.
lim lim
u(x) =
−
− −
x→ 1 x→
.
−
0.222222.... Because the output values appear
.
2/9. Because the output values appear to become
lim
−
x→ 2/9
2 +
3 x 3 x
entered in the
+ +
2
9 x 11 x 2
F2 [Zoom] 4 [ZoomDec]
is not very helpful.
lim
u(x) = 0.429, we are only interested in
−
x→ 1
−
1. So, choose values very near to
− − − −
To numerically estimate
u(x) = 0.429, we estimate that
+
1
To numerically estimate
u(x) → ∞.
lim
−
−
x→ 2/9
To numerically estimate
u(x) → − ∞. Thus,
−
location
y 1
or
−
1
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Chapter 1
1.
lim
u(x) =
+
−
x→ 1
lim
u(x) = 0.429.
−
x→ 1
A graph can