Incorrect limit

[Alexmaster350]

Typing the limit of x^3*cos(x)/(e^x-e^(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.

[ijabbott]

(01-10-2019 05:34 PM)Alexmaster350 Wrote:  Typing the limit of x^3*cos(x)/(e^x-e^(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.

[roadrunner]

limit(taylor((x^3*cos(x)/(e^x-e^(π/2))),x = (π/2),0,polynorm),x,π/2)

give the correct answer.

???

-road

[Albert Chan]

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 // ???

[parisse]

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.