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wrong limit ?

• To: mathgroup at smc.vnet.net
• Subject: [mg76734] wrong limit ?
• From: ventu <nuclearVentu at gmail.com>
• Date: Sat, 26 May 2007 04:43:44 -0400 (EDT)

Hi !
Here's my problem (mathematica 5.0,5.1,5.2):

Limit[Coth[xB], B -> +Infinity]

it doesn't understand.
mmh. ok I try then:

Limit[Coth[x B], B -> +Infinity, Assumptions ->  Im[x] == 0]

1

WRONG ! In fact:

Limit[Coth[x B], B -> +Infinity, Assumptions ->  Im[x] == 0 && Re[x] <
0]

-1

Indeed the correct result should be sign(x). And I couldn't find a way
to get it right.
Do I mistake something?

Thank you in advance,

Davide