226 Appendix D: A Detailed Look at _
Execute _again:

 

Keystrokes

Display

¥

 

0 v

0.0000

1

1

´vB

4.0681

)

4.0681

)

0.0000

Run mode.

Initial estimates.

The desired root.

A previous estimate of the root.

Value of modified f(t) at root.

After 4.0681 seconds, the ridget is at a height of 107 ± 0.5 meters. This solution, although different from the previous answer, is correct considering the uncertainty of the height equation. (And this solution is found in just under half the time of the earlier solution.)

Interpreting Results

The numbers that _ places in the X-, Y-, and Z-registers help you evaluate the results of the search for a root of your equation.* Even when no root is found, the results are still significant.

When _ finds a root of the specified equation, the root and function values are placed in the X- and Z-registers. A function value of zero is the expected result. However, a nonzero function value is also acceptable because it indicates that the function's graph apparently crosses the x- axis within an infinitesimal distance from the calculated root. In most such cases, the function value will be relatively close to zero.

*The number in the T-register is the same number that was left in the Y-register by the final execution of your function subroutine. Generally, this number is not of interest.