Solving inequalities

[ftneek]

Hello, I was trying some problems from file:///Applications/Xcas.app/Contents/u...el009.html when I think I came across a discrepancy when compared with the output of Wolfram alpha on exercise 8, specifically the third limit given and part 2 of the exercise.

When I use the command

Code:

solve(Abs[Limit[(1+1/x)^x,x->+∞]-(1+1/x)^x]<10^-3)

on Wolfram alpha I get the solutions x<-1360.057606 or x>1358.224273

When I use cas on the hp prime, I only get one solution {x>1358.22430275} (Is there a way to copy a plain text representation of a calculation on my virtual calculator to my computer's clipboard? I'm using the most up to date version of the Mac version if it makes a difference)

When I used Xcas on a Firefox browser, I get list[-254822177851,x>1358.22428235]
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)

Why does hp prime cas only return one interval? Why is the first solution by Xcas very small (although maybe technically correct)? By the way, when I change < to <=, Wolfram gives x<=-1360.06 or x>=1358.22, Xcas gives list[(x>=(-198574405166)) and (x<-1)] but hp prime cas gives [] no solution? And when I change < to just =, prime seems to match Wolfram alpha with x≈-1360.06 and x≈1358.22, but Xcas just gives list[1358.22430144]. Why don't the results from Xcas, prime, and Wolfram alpha all agree? If it's a bug, is there any chance of it being fixed in the future?

Update: I just tried repeatedly executing the same expression on Xcas, and each time it gave a different result, cycling between [] no solution, 1 solution (around 1358), 2 solutions (correct) solutions, and a list of solutions (only 1 looks right). I just tried the same thing on my virtual calculator, copying the expression and evaluating it again, and it seems to cycle like Xcas. I'm using the most up to date version of the virtual calc for Mac, and will try testing on my physical prime tomorrow and give an update if the results are any different than the virtual.