Hey, I've got a question... If I have 8 cards in my hand and cast Demonic Tutor, bringing my total to 7 cards, is there any way I can draw a card with the Library before I search for my card bringing me back up to 8?
Yes. Demonic Tutor leaves your hand by going on the stack. Respond to your own tutor by activating library, draw a card, then tutor resolves.
You can also use library tricks with the Enlightened,Mystical and Vampiric Tutors. Here you do the opposite. Start with 7 cards in hand, tap library, putting it's ability on the stack, then tutoring in response. this works beacuse the seven card test only happens on announcement. This puts the tutored for card right in your hand.
What about Worldly Tutor? Or Planar Portal? :^)
Worldy Tutor works for the same reason as Enlightened, Mystical and Vampiric.
Planar Portal would not, as using the Portal doesn't mess with your hand size, so you could use the library before or after.