Dan-san, エリックsan,
kon'nichiwa
Thank you very much for spot-on explanations, エリックsan!!
Just to add a little note (hope this won't confuse you), "...beki" can be used with negative form of verbs.
However, it's more common to use "[verb dictionary form] beki dewa arimasen".
Connotations are, of course, different.
ex.
1. ashita wa dekakeru beki dewa arimasen.
2. ashita wa dekake nai beki desu.
The sentence 1 is practically saying "You shouldn't go out tomorrow" while the sentence 2 implies more like
"You should stay at home without going out". Obligations/orders that this speaker is giving are
sentence 1: denying the possibility of going out
sentence 2: ordering not to go out.
Like Eric-san wrote, "beki" is a very strong word, so if it's used in affirmative sentence, it's a very strong demand
or recommendation almost like an order. Negative sentence means it's denying this strong message.
Natsuko(奈津子),
Team JapanesePod101.com