Visualizing The Limiting Process; Tangent Lines And Instantaneous Rates Of Change - Texas Instruments TI-84 Plus Manual

TI-83, TI-83 Plus, TI-84 Plus Guide
VISUALIZING THE LIMITING PROCESS This section of the Guide is optional, but it
might help you understand what it means for the tangent line to be the limiting position of
secant lines. Program
points on a curve y = f(x). The program also draws the tangent line at the point (a, f(a)). We
illustrate with the graph of the function T that was used in the previous two sections, but you
can use this program with any graph. (Program
Caution: Before using program
entered in the
Y1
tangent line, you must first draw a graph clearly showing the function, the point of tangency
(which should be near the center of the graph), and a large enough window so that the close
points on either side of the point of tangency can be viewed.
−
Have T(x) =
and set
WINDOW
Press
GRAPH
the location of program
look like the one shown on the right.)
Press
ENTER
function in
Y1
and press
ENTER .
the point of tangency. (For this illustration, choose x = 4.)
Press
ENTER .
enter to see secant lines drawn between the point of tangency
and close points to the left. Press
will draw.)
When you finish looking at the graph, press
continue. The next message that appears tells you to press enter
to see secant lines drawn between the point of tangency and
close points to the right. (Again, five secant lines will draw.)
Press
ENTER .
Press
ENTER
press
ENTER
curve at x = 4.
As you watch the graphs, you should notice that the secant lines are becoming closer and
closer to the tangent line as the close point moves closer and closer to the point of tangency.

TANGENT LINES AND INSTANTANEOUS RATES OF CHANGE

calculator gives results that are not the same as the mathematical results you expect. This does
not mean that the calculator is incorrect – it does, however, mean that the calculator
programming is using a different formula or definition than the one that you are using. You
need to know when the calculator produces a different result from what you expect from our
formulas.
Copyright © Houghton Mifflin Company. All rights reserved.
is used to view secant lines between a point (a, f(a)) and close
SECTAN
SECTAN
location of the list. In order to properly view the secant lines and the
Y=
2
0.804x + 11.644x + 38.114 in
Xmin = 0, Xmax = 7, Ymin = 30, Ymax = 90.
. Press and the number or letter next to
PRGM
.
SECTAN (Your program list may not
to start the program. If you forgot to enter the
or to draw its graph, enter
At the next prompt, type the input value at
The next message that appears tells you to press
ENTER .
to continue the program. You are next told to
to see a graph of the line that is tangent to the
is Program Appendix of this Guide.)
SECTAN
, a function (using x as the input variable) must be
. Next, press
Y1
. Otherwise, type
2 1
(Five secant lines
to
ENTER
Sometimes the
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