Using the EVAL Program
Use the EVAL program to create a table of values for
the function f (x) = x
x
. (Refer to the table in Exam-
ple 5 in the text.)
Solution. We assume that you already have placed
the EVAL program into your calculator. Input Y
1
= x
x
and execute the EVAL program. The program requests
x =. Input 0.1 and press the ENTER key. The pro-
gram returns .7943282347 and requests another x =.
Continue in this manner to complete the table.
Section 3.2 in Text
• Drawing a Tangent Line on a Curve
• The Program SEC
Draw a Tangent Line Using DRAW
Graph y = 16x
2
on a screen with dimensions [0, 1.88] by
[0, 64]. Draw the tangent line to the graph of the curve
when x = 1 and note the slope. What is the instanta-
neous velocity when x = 1? Refer to Exploration 2 in
the text.
Solution. We can draw the tangent line from the
DRAW menu on the TI-82. Enter Y
1
= 16x
2
into the
function menu. Set the dimensions of the window to
[0, 1.88] by [0, 64] and graph. Now press the keys 2nd
DRAW 5 . Move the cursor so that X = 1. Then
press ENTER . A tangent line is drawn at x = 1. The
slope is shown on the bottom as dy/dx = 32.
The Program SEC
The program SEC given in the Program section of this
manual graphs y = f(x), the tangent line at the indi-
cated point, and a sequence of secant lines for values of
h approaching zero and thus demonstrates Figure 3.34
of the text. Use this program on the function y = x
2
at x = 1 with a window of dimensions [.8, 2] by [0, 4].
Solution. Input Y
1
= x
2
. Use a window with dimen-
sions [.8, 2] by [0, 4]. Execute the SEC program.
The program requests a value for x. Press the keys
1 ENTER . The program requests a value for N.
(This will be the number of secant lines drawn.) Press
the keys 1 0 ENTER . Graphs of y = x
2
and the
tangent line at x = 1 are drawn.
Now each time you press the ENTER key a secant
line will be drawn with h smaller. You see the secant
lines getting closer and closer to the tangent line.
43
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