Numerically Estimating The Limit At A Point - Texas Instruments TI-84 Plus Manual

TI-83, TI-83 Plus, TI-84 Plus Guide
Have u(x) =
10
(Be certain that you remember to enclose both the numerator
and denominator of the fraction in parentheses.) A graph drawn
with
ZOOM 4 [ZDecimal]
We estimated the limit as x gets very large or very small to be
0.3. Now, u(0) = 0, and it does appears from the graph that
u is never negative. To obtain a better view of the outputs, set a
with values such as
WINDOW
and
Ymax = 0.35.
To examine the limit as x gets larger and larger (i.e., to zoom out
on the positive x-axis), change the
view the graph with
Xmax = 1000,
and hold down
TRACE
outputs. The output values confirm our numerical estimate.
Repeat the process as x gets smaller and smaller, but change
rather than
Xmin
the right was drawn with
and
Ymax = 0.35.
graph screen to view some of the outputs and confirm the
numerical estimates.
NUMERICALLY ESTIMATING THE LIMIT AT A POINT Whenever you numerically
estimate the limit at a point, you should again set the
using the function u(x) =
Enter u(x) =
9
Have
TBLSET
return to the table.
Delete the values currently in the table with
cally estimate
and closer to,
appear to become larger and larger, we estimate that the limit
does not exist and write
Copyright © Houghton Mifflin Company. All rights reserved.
2
+
3
x x
in the
Y1
2
+ +
3 2
x x
is a starting point.
Xmin =
Press .
GRAPH
WINDOW
change the
GRAPH ,
view the graph with
GRAPH ,
on each graph screen to view the
►
after drawing each graph. The graph to
Xmax
−
Xmin = 10,000, Xmax = 10, Ymin = 0,
Press and hold
TRACE
3
x
x +
9 2
3
x
in some list location, say
Y=
x +
2
set to and press
Ask, 2nd
lim
u(x), enter values to the left of, and closer
−
−
2/9
x→
−
−
2/9 = 0.222222.... Because the output values
u(x) → ∞.
lim
−
−
2/9
x→
location of the list.
Y=
−
10, Xmax = 10, Ymin = 0,
so that
Xmax = 100,
so that
WINDOW
and so forth. Press
while on each
◄
to
TABLE
.
Y1
to
GRAPH (TABLE)
To numeri-
DEL .
mode. We illustrate
ASK
37