bug xCas limit

[robmio]

Hi everyone, maybe I discovered a bug in xCas: the following limit results in "zero" instead of "-1":

limit (cos (x) / (x-pi / 2), x = pi / 2)

Try to calculate it both with "HP PRIME" and with Giac xCas.

Best regards, Roberto

[Albert Chan]

For XCas, replacing variable x to others seems to help.

XCas> f(a) := limit(cos(t+pi/2-a)/(t-a), t=a)
XCas> f(pi/2)   → -1
XCas> f(pi/3)   → -1
XCas> f(0)       → -1

Cas> f(a) := limit(cos(t+pi/2-a)/(t-a), t=a)
Cas> f(pi/2)      → 0
Cas> f(pi/3)      → 0
Cas> f(0)          → -SIN(a)/a       ???

[Albert Chan]

Another XCas limit bug (for HP Prime Cas, limit crashes)

XCas> asinh(x)       → ln(x+sqrt(x^2+1))
XCas> asinh(i)        → ln(i) = ln(abs(i)) + i*arg(i) = i*pi/2

XCas> limit(asinh(i*x), x=1)

"Limit: Max order reached or unable to make series expansion Error: Bad Argument Value"

Udpate Nov 10,2022:

I upgraded to XCas 1.9.0-22 (win32).
OP bug now fixed. However, asinh limit bug remain.

XCAS> limit (cos(x)/(x-pi/2), x = pi/2)      → -1