Help with Limit and Integration

1. Find the limit: lim x->0

(cos 3x)^1/x (Hint: use logarithmic method)

2. let f(x)=(5x^2 + 1)/((x-1)(x+1)^2) Find a,b,c such that f(x)=(a/(x-1))+(b/(x+1))+(c/(x+1)^2), and use the decomposition to evaluate the integral /f(x)dx

3. Evaluate improper integral: from 0-infinity xe^-x dx(hint: use integration by parts)

4. Evaluate improper integral: from0-2 (dx/(sqrt(4-x^2))

5. The region R enclosed by the curves y-x/4 and y^2=x is rotated about the y-axis. Find the volume of the resulting solid.

Thank you very much for your help