Texas Instruments TI-82 Manual page 34

34
G T G : TI-82
RAPHING ECHNOLOGY UIDE
Figure 2.85: Newton's method
Technology Tip: Newton's Method is sensitive to your seed value for x, so look carefully at the function's graph to
make a good first estimate. Also, remember that the method sometimes fails to converge!
You may want to save the Newton's Method formula as a short program. See your calculator's manual for further
information on programming the TI-82.
2.12 Integration
2.12.1 Approximating Definite Integrals: The TI-82 has the function fnInt( in the MATH menu to approximate an
1
∫
2
integral. So to find a numerical approximation to cos x dx with a tolerance of 0.001 (which controls the accuracy
0
2
of the approximation), press MATH 9 COS x , , 0 , 1 , .001 ) ENTER as shown in Figure 2.86. The
X,T,θ X,T,θ
format of this command is fnInt(expression, variable, lower limit, upper limit, tolerance). The same integral is
also approximated in Figure 2.86 using a tolerance of 0.00001, the TI-82's default that is used when no other
tolerance is specified.
Figure 2.86 fnlnt(
2.12.2 Areas: You may approximate the area under the graph of a function y =f (x) between x = A and x = B with
2
your TI-82. For example, here are keystrokes for finding the area under the graph of the function y = cos x between
1
∫
2 2
x = 0 and x = 1. This area is represented by the definite integral cos x dx. So graph f (x) = cos x and press 2nd
0
CALC 7. Use the arrow keys to trace along the curve to the lower limit and press ENTER; then trace again to the
upper limit (see Figure 2.87) and press ENTER. The region under the graph between the lower limit and the upper
-5
limit is shaded and the area is displayed as in Figure 2.88. The TI-82 uses fnInt( with the default tolerance of 10 in
this calculation.
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