Unable to evaluate the following limit

06022020, 04:23 AM
Post: #1




Unable to evaluate the following limit
I want to find the limit of the piecewise function as follows:
And here are the limit to find out The expected answer is 1 and 1/3 respectively. In the calculator with latest firmware (2020 01 21), it returns both limits to 0 which is not correct. In the emulator (as in this picture), it provides error message for the first one, but provide the correct answer for the second one. I verified this with TI Nspire, it provide the correct answer. could you please help fix this issue. 

06022020, 02:03 PM
Post: #2




RE: Unable to evaluate the following limit
Can you give the input as a commandline? Pictures are nice but can not be copied/pasted.


06022020, 02:57 PM
(This post was last modified: 06022020 02:59 PM by pinkman.)
Post: #3




RE: Unable to evaluate the following limit
Definition of f1:
f1(x):=PIECEWISE(x>1,x^2,(x>0) AND (x<=1),x1,x<=0,0) The first limit: limit(f1(x^2),x,0,1) The second limit: limit((f1(x1))/(x+2),x,1,1) 

06022020, 04:19 PM
Post: #4




RE: Unable to evaluate the following limit
In the simulator if you replace x^2 with x*x you get 1 for the first limit:
limit(f1(x*x),x,0,1) > 1 road 

06022020, 05:35 PM
(This post was last modified: 06022020 05:37 PM by victorvbc.)
Post: #5




RE: Unable to evaluate the following limit
(06022020 04:19 PM)roadrunner Wrote: In the simulator if you replace x^2 with x*x you get 1 for the first limit: Apparently the expression x^2<=0 simplifies to false (??). It works with x*x because the calculator doesn't automatically simplify that, so the limit takes the expression x*x<=0. 

06022020, 06:08 PM
Post: #6




RE: Unable to evaluate the following limit
Thanks, this is now fixed in the source code.


06022020, 06:59 PM
Post: #7




RE: Unable to evaluate the following limit
By the way, I'm not a big PRIME user, but let me say offtopic a thank you to Bernard for all his work on the CAS of multiple HP machines.


06022020, 10:33 PM
Post: #8




RE: Unable to evaluate the following limit
(06022020 05:35 PM)victorvbc Wrote:(06022020 04:19 PM)roadrunner Wrote: In the simulator if you replace x^2 with x*x you get 1 for the first limit: I don’t see it: how the 3rd condition could ever be true, even with x*x? 

06022020, 10:50 PM
Post: #9




RE: Unable to evaluate the following limit  
06032020, 06:20 PM
Post: #10




RE: Unable to evaluate the following limit
Thank you parisse for fixing this. Thank you all for your help.


06032020, 07:59 PM
(This post was last modified: 06032020 07:59 PM by pinkman.)
Post: #11




RE: Unable to evaluate the following limit
(06022020 10:50 PM)victorvbc Wrote:(06022020 10:33 PM)pinkman Wrote: I don’t see it: how the 3rd condition could ever be true, even with x*x? Yes I know that, but I don’t understand what you did understand: Quote:Apparently the expression x^2<=0 simplifies to false (??).What simplification could lead the algorithm to understand x*x is more <=0 than x^2? 

06032020, 08:14 PM
(This post was last modified: 06042020 01:06 PM by victorvbc.)
Post: #12




RE: Unable to evaluate the following limit
It's not about the expression itself, just that the calculator doesn't evaluate x*x<=0 to false, like it does with x^2<=0. Only if you simplify it.
Here's a screenshot to illustrate my point: So my theory is the limit program doesn't have any problems with handling the inequality x*x<=0, but it can't handle the direct false from x^2<=0. That's why it throws the "Unable to handle when condition is false error". Edit: The correct simplification, of course, should just be x^2<=0. Because if x is zero (or some imaginary number), the resulting expression is true. 

06032020, 09:00 PM
Post: #13




RE: Unable to evaluate the following limit
Thanks, I didn’t get it, now I do!


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