HP 40g hp 39g+ (39g & 40g)_mastering the hp 39g+_English_E_F2224-90010.pdf - 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 3 3000 , 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. ∫ a x2 dx = 1000 0    x3 3 a  0 = 1000 a3 = 1000 3 a = 3 3000 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 10-12 precision, you need only consider the two contrasting results of ASIN(1) and 1 × 9 shown to the 9 right. 311