HP 40gs hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 93

Plotting to find guesses

Page 93 highlights

hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM If Solve could not find a solution, you will see one of the following two messages. Message Bad Guess(es) Constant? Condition The initial guess lies outside the domain of the equation. Therefore, the solution was not a real number or it caused an error. The value of the equation is the same at every point sampled. HINT It is important to check the information relating to the solve process. For example, the solution that the Solve aplet finds is not a solution, but the closest that the function gets to zero. Only by checking the information will you know that this is the case. The Root-Finder at work You can watch the process of the root-finder calculating and searching for a root. Immediately after pressing to start the root-finder, press any key except . You will see two intermediate guesses and, to the left, the sign of the expression evaluated at each guess. For example: + 2 2.219330555745 - 1 21.31111111149 You can watch as the root-finder either finds a sign reversal or converges on a local extrema or does not converge at all. If there is no convergence in process, you might want to cancel the operation (press ) and start over with a different initial guess. Plotting to find guesses The main reason for plotting in the Solve aplet is to help you find initial guesses and solutions for those equations that have difficult-to-find or multiple solutions. Consider the equation of motion for an accelerating body: X = V0T + AT 2 2 Solve aplet 7-7

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Solve aplet
7-7
If Solve could not find a solution, you will see one of the
following two messages.
HINT
It is important to check the information relating to the
solve process. For example, the solution that the Solve
aplet finds is not a solution, but the closest that the
function gets to zero. Only by checking the information
will you know that this is the case.
The Root-Finder
at work
You can watch the process of the root-finder calculating
and searching for a root. Immediately after pressing
to start the root-finder, press any key except
.
You will see two intermediate guesses and, to the left, the
sign of the expression evaluated at each guess. For
example:
+ 2 2.219330555745
– 1 21.31111111149
You can watch as the root-finder either finds a sign
reversal or converges on a local extrema or does not
converge at all. If there is no convergence in process, you
might want to cancel the operation (press
) and start
over with a different initial guess.
Plotting to find guesses
The main reason for plotting in the Solve aplet is to help
you find initial guesses and solutions for those equations
that have difficult-to-find or multiple solutions.
Consider the equation of motion for an accelerating
body:
Message
Condition
Bad Guess(es)
The initial guess lies outside the
domain of the equation.
Therefore, the solution was not a
real number or it caused an error.
Constant?
The value of the equation is the
same at every point sampled.
2
2
0
AT
T
V
X
+
=
hp40g+.book
Page 7
Friday, December 9, 2005
1:03 AM