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

Delete the values currently in the table
lim
u(x), enter values to the right of, and closer and closer
+
−
2/9
x→
−
to, 2/9. Because the output values appear to become larger and
larger, we estimate that

GRAPHICALLY ESTIMATING THE LIMIT AT A POINT

estimate a limit at a point or to confirm a limit that you estimate numerically. The procedure
usually involves zooming in on a graph to confirm that the limit at a point exists or zooming
out to validate that a limit does not exist. We again illustrate using the function
3
x
u(x) = .
x +
9 2
Have the function u(x) =
list, say
Y= Y1
ZOOM 6 [ZStandard]
To confirm that
x→
are near to and on either side of
Choose input values close to
experiment with different y values until you find an appropriate
vertical view. Use these values to manually set a window such as
that shown to the right. Draw the graph with
The vertical line appears because the
TI-83 is set to
the TI-83 in
Dot
function in the
Y1
(see page A16) and redraw the graph.
It appears from this graph that as x approaches
without bound and that as x approaches
without bound. Choosing smaller
tracing the graph as x approaches
Graphically Estimating a Limit at a Point when the Limit Exists: The previous illustrations
involved zooming on a graph by manually setting the window. You can also zoom with the
menu of the calculator. We next describe this method by zooming in on a function for
ZOOM
which the limit at a point exists.
Have the function h(x) =
that we want to estimate
38
lim u(x) →
+
−
2/9
x→
3
x
entered in some location of the
x +
9 2
. A graph drawn with
ZOOM 4 [ZDecimal]
is not very helpful.
lim lim
u(x) and
−
− −
2/9 2/9
x→
−
2/9.
−
0.222222... for the x-view and
mode. Place
Connected
mode or place the
list in mode
Y= Dot
−
Ymin
−
2/9 from either side confirms this result.
2
+
3 3
x x
2
+ + 2
9 11
x x
lim
h(x).
−
1
x→
To numerically estimate
.
− ∞.
or
u(x) do not exist, we are interested in values of x that
+
.
GRAPH
−
2/9 from the left that the output values increase
2/9 from the right that the output values decrease
values and larger
Ymax
entered in the location of the
Y1
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Chapter 1
A graph can be used to
values in the and
Window
list. Suppose
Y=