HP 15c Scientific manual 000

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. Enter the subroutine from page 184 that calculates the height of the ridget. This subroutine can be used in a new function subroutine to calculate

		f(t) = h(t) – 107.
The following subroutine calculates f(t):
Keystrokes	Display
¥	000–		Program mode.
´b B	001–42,21,12		Begin with new label.
G A	002–	32 11	Calculates h(t).
1	003–	1
0	004–	0
7	005–	7	Calculates h(t) – 107.
-	006–	30
n	007–	43 32