Incorrect limit

01102019, 05:34 PM
Post: #1




Incorrect limit
Typing the limit of x^3*cos(x)/(e^xe^(pi/2)) as x tends to pi/2 on the HP Prime gives an answer of zero when it should be pi^3*e^(pi/2)/8. Is there a reason for this and I am making a mistake or is it not working properly? Nothing is saved in the variable x.


01102019, 06:35 PM
Post: #2




RE: Incorrect limit
(01102019 05:34 PM)Alexmaster350 Wrote: Typing the limit of x^3*cos(x)/(e^xe^(pi/2)) as x tends to pi/2 on the HP Prime gives an answer of zero when it should be pi^3*e^(pi/2)/8. Is there a reason for this and I am making a mistake or is it not working properly? Nothing is saved in the variable x. I think you are correct and the calculator is wrong. — Ian Abbott 

01102019, 06:51 PM
Post: #3




RE: Incorrect limit
limit(taylor((x^3*cos(x)/(e^xe^(π/2))),x = (π/2),0,polynorm),x,π/2)
give the correct answer. ??? road 

01102019, 07:34 PM
(This post was last modified: 01102019 07:58 PM by Albert Chan.)
Post: #4




RE: Incorrect limit
Pulling the x³ factor help ...
(pi/2)³ * limit(cos(x)/(e^x  e^(pi/2)), x=pi/2) ==> −(pi/2)³ / exp(pi/2) BTW, playing with this limit discovered another bug: f(x) := (e^x  e^(pi/2)) / cos(x) limit(f(x), x=pi/2, −1) => exp(pi/2) // ok limit(f(x), x=pi/2, +1) => exp(pi/2) // ok limit(f(x), x=pi/2, 0) ==> 0 // ??? 

01102019, 07:45 PM
Post: #5




RE: Incorrect limit
Indeed you have found a bug, caused by partfrac bad rewriting the expression.
I have committed a fix. If you doubt about a limit, it is a good idea to call series at the same point, because limit tries to resolve fast by substitution and it may miss some cancellations, while series does not. 

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