1. Limit [x->1] [(e^x-e)*(x-1)] = e

How to solve ? Derivation (L'Hopital's rule) don't get anything useful - it remains [0/0].

2. Limit [x->0] [Ln[Cos[x]] / x^2] = -1/2

Any idea ?

3. Limit [x->Inf] [(x^3+2x-1)^(1/3) / (x+2)] = 1

How to solve ?

4. [a^b]' = b*Ln[a]*[a]'

Is it right?