Rounding Off; Rule Of Thumb For Determining Limits From Tables; Graphically Estimating End Behavior - Texas Instruments TI-84 Plus Manual

Press
2nd WINDOW (TBLSET).
location by placing the cursor over
(Remember that the other settings on this screen do not matter
if you are using
Press
2nd GRAPH (TABLE).
by placing the cursor over the first
pressing
DEL
increasingly large values of x. (Note: The values you enter do
not have to be those shown in the text or these shown to the
right provided the values you input increase without bound.)
CAUTION: Your instructor will very likely have you write the table you construct on paper.
Be certain to highlight the rounded values in the output column of the table and look on the
bottom of the screen to see what these values actually are.
ROUNDING OFF: Recall that rounded off (also called rounded in this Guide) means that if
one digit past the digit of interest is less than 5, other digits past the digit of interest are
dropped. If one digit past the one of interest is 5 or over, the digit of interest is increased by 1
and the remaining digits are dropped.
RULE OF THUMB FOR DETERMINING LIMITS FROM TABLES: Suppose that you
are asked to give
x→
you see that the output is the same value to one more decimal place (here, to 4 decimal places)
for 3 consecutive outputs. Then, round the last of the repeated values 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, to 3 decimal places,
Delete the values currently in the table with
the negative end behavior of u, enter negative values with
increasingly large magnitudes. (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 0.2999... appears three times in a row, we estimate
CAUTION: It is not the final value, but a sequence of several values, that is important when
determining limits. If you enter a very large or very small value, you may exceed the limits of
the calculator's capability and obtain an incorrect number. Always look at the sequence of
values obtained to make sure that all values that are found make sense.
GRAPHICALLY ESTIMATING END BEHAVIOR The graph of the function u in Example
3 of Section 1.4 in Calculus Concepts can be used to confirm our numerically estimated end
behavior. Even though the
functions, the graph of u is lost if you use
manually set the window to zoom out on the horizontal axis.
36
Choose
Ask
.)
Ask
Delete any values that appear
value and repeatedly
X
. To numerically estimate
lim
u(x) accurate to 3 decimal places. Observe the
∞
lim
u(x) = 0.300. We now need to estimate
∞
x→
menu of the calculator can be used with this process for some
ZOOM
Option 3
in the
Ask Indpnt:
and pressing
ENTER .
lim
u(x), enter
∞
x→
To estimate
DEL .
in the menu (
ZOOM
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Chapter 1
values in the table until
Y1
lim
u(x).
− ∞
x→
lim
u(x) = 0.300.
− ∞
x→
). We therefore
Zoom Out