1. lim x->0 of (a^x - b^x)/x = ?

I see that as x goes to zero, the top goes to 1-1 which would make the whole thing zero, but at the same time the bottom goes to 0 but you can't divide by zero of course. I'm not sure if I'm supposed to do some voodoo to remove the x from the bottom, or if there's some concept I should explain. Maybe I need to use the definition of a limit somehow?

2. lim x->9 of (1-x)^(1/x). Again the same type of situation. 1^(anything) is 1, but at the same time the exponent is going to (1/0).

There is also a third problem. If there is something different I need to know about this I would appreciate some tips, but if you think I can get it once I learn the previous two then never mind it.

3. lim x->infinity [sqrt(x)logx]/x

Thank you,

gsxrk3