Solving inequalities

[Albert Chan]

(11-16-2022 10:45 AM)ftneek Wrote:  The command I entered on Xcas is

Code:

f(x):=(1+1/x)^x ;
solve(abs(limit(f(x),x=+infinity)-f(x))<10^-3)

Solver probably added some random elements to guess, thus getting different results.
Negative solution is tougher, since f(x) = negative ^ negative = complex

On XCas 1.5.0-63 (win32) (old version), I get different results, with repeated solve.

[((x>1358.2242733) and (x<4.84957600044e+12))]
[((x>1358.22427348) and (x<4.15614031773e+12))]
[x>1358.22427318]
[x>1358.22427339]
[x<-1360.05760617,x>1358.22427263]

I get the correct result on the fifth tries.
The problem is ... we don't know which one to pick.

On XCas 1.9.0-22 (win32) (new version), it crashes every time.

On HP emulator Build 2.1.14181 (2018 10 16) (very old), surprisingly, I get good answer for every solve.
I had never bother to upgrade

{x<−1360.05760747,x>1358.22428117}
{x<−1360.05761507,x>1358.22429144}
{x<−1360.05760716,x>1358.22430358}
{x<−1360.05761158,x>1358.22427617}
{x<−1360.05761261,x>1358.22429356}

Update Nov 22, 2022:

I tried XCas 1.9.0 again. This time no crash, given similar result to XCas 1.5.0