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\-,
\./
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\,
\-.
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In
most situations,
the
calculated
root is an
accurate estimate
of
the
theoretical,
infinitely
precise
root of the equation.
An
'idealr solution
is one for which f(x)
-
0.
However,
a
non -zero
value
for f(x)
is often
also
acceptable,
because
it
results
from
approximating numbers
with
limited
(12-digrt)
precision.
The
Solver can deal
with
a
wide variety
of
complex
situations.
Results
of
an
iterative solution
are
divided
into four major situations-cases
t,
2, 3, and
4.
Gases Where a Root
ls
Displayed lGases
la
and
lbl
In
case
1,
the Solver automatically displays the
calculated
root.
Table
B-1
describes
the two
case
1 situations. (Also
see
figure 5-1 on
Page
L
14.)
For
case
la,
the
calculated
root
sets
f(x)
exactly
equal
to
0. For
case
lb,
the
calculated
root is a 12-digit number
adjacent
to the
place where
the function's graph
crosses
the
r-axis.
Cases La
and
Lb
are
differenti-
ated
by
pressing
the menu
k.y
for
the unknown after the root
has
been
displayed.
For
case
lb
solutions, the
HP-27S displays
the
values
of
g(x)
(LEFT)
and
h(x)
(RIGHD.
\-.
Table
B-1
.
Gase
I
Solutions
Gase
Signs
of
J(xI
for
Final Estimates
Gomparision
of
Final Estimates
Trends in f(xl
Case
1a
Case
1b
f
(x):o
Opposite
Neighbors
f(x) tor
the estimates
have
not
been
strongly
diverging
from
zero as
x
ap-
proaches
the two
neighbors
from
both
sides.
B:
tore
About
the
Solver 2ll
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