I need help finding the limits of these expression using L'Hospital's rule.

1. lim x --> 1 {x^a - ax + a -1/(x -1)^2}

2. lim x --> 0+ {sqrt(x) lnx}

3. lim x --> 0 {cot2x sin6x}

4. lim x --> infinity {x^3e^-x^2}

5. lim --> infinity {xe^1/x - x}

6. lim --> infinity {x - lnx}

5. lim --> 0+ {x^x^2}