HP 39g Master Manual page 311

The two values at the top of the screen represent the calculator's successive
approximations to the true solution. The chances are that one will have a '+'
symbol to the left of it, while the other has a '-'. This is telling you that the '+'
value is greater than required, while the '-' value is smaller. As you watch you
should see the two values converge to the true answer.
But is it? The true answer is actually
as is shown right. Unless you realized that the
value supplied was a cube root it is unlikely
that you would get this exact solution.
Algebraically, the solution is shown to the right.
On most calculators there is no way to obtain this exact
answer because the calculator doesn't use algebra.
However, the CAS or Computer
Algebra System on the hp 40g
does use algebra! As you can
see in the screen shots to the
right, the CAS on the hp 40g is perfectly
capable of giving you the algebraically
correct answer, and it does it by
following the same rules that you do.
The CAS on the hp 40g is based on a program
called Erable, originally written by Bernard Parisse for
the HP49G, which was then adapted for the hp 40g. It
is an amazingly powerful CAS which will let you
perform virtually any mathematical manipulation you
might need.
For an example of the fundamental
difference between working in the CAS,
with its exact mode & infinite precision,
and working in the normal HOME view, in
approximate mode with 10
need only consider the two contrasting
results of ASIN(1) and
right.
3000 ,
3
-12
precision, you
1
× shown to the
9
9
311
∫ a
=
2
x dx 1000
0
a
 
3
x
=
 
1000
 
3
0
3
a
=
1000
3
=
3
a 3000