Function intersection

[rawi]

RobbiOne wrote:

Quote:It is Not a bug, two floating point numbers gotten from square and log algorithms with a finite precision digits will be never exactly the same... compare with == always fails (99.99%)

Despite this is formally correct I do not think that this is a convincing argument. With the same argument most equations could not be solved numerically because - just for example - there is no floating point number with a finite precision which solves exactly SQRT(2)-X=0.

One problem for those two functions is that the curves do not intersect but touch each other.
The Prime indeed does not find the touch point. It not even finds the zero point of the combined function x^2-2-ln(x^2-1) which touches the x-axis.

Compared to this other calculators find the solutions. The TI N'spire CXII CAS finds the touch points as well as the zero points of the combined function. As well the much older TI-89 Titanium finds the touch points of the two curves and the zero point of the combined function. And even the DM 42 finds the zero point of the combined function.

So it seems that this indeed is a weakness of the HP Prime. It would be interesting whether this is with other functions that touch each other as well.