224 Appendix D: A Detailed Look at _
the root 1.0000 is found for initial estimates of 1 and 2. By recognizing
situations in which round-off error may influence the operation of
_, you can evaluate the results accordingly and perhaps rewrite the
function to reduce the effects of round-off.
In a variety of practical applications, the parameters in an equation—or
perhaps the equation itself—are merely approximations. Physical
parameters have an inherent accuracy (or inaccuracy). Mathematical
representations of physical processes are only models of those
processes, accurate only to the extent that the underlying assumptions
are true. An awareness of these and other inaccuracies can be used to
your advantage. By structuring your subroutine to return a function value
of zero when the calculated value is negligible for practical purposes, you
can usually save considerable time in finding a root with _—
particularly for cases that would normally take a long time.
Example: Ridget hurlers such as Chuck Fahr can throw a ridget to heights
of 105 meters and more. In fact, Fahr’s hurls usually reach a height of
107 meters. How long does it take for his remarkable toss, described on
page 184 in Section 13, to reach 107 meters?
Solution: The desired solution is the value of t at which h = 107. The
subroutine from page 184 calculates the height of the ridget, h(t). This
subroutine can be used in a new function subroutine to calculate
f(t) = h(t) − 107.
The following subroutine calculates f(t).
Enter this subroutine after
entering the subroutine from page 184:
| ¥
021- 43 32
Program mode.
´ b B
022-42,21,12
Begin with new label.
G A
023- 32 11
Calculates h(t).
1 024- 1
0
025- 0
7 026- 7
Calculates h(t) − 107.
-
027- 30
| n
028- 43 32
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