I meant lots of issues, sorry

The problem says to : Evaluate the improper integrals. Show the proper use of limits.

The integral of 1/(x^2-9) from 3 to infinity.

I can get it into the limit form and solve the integral part but I can't solve the limit. It works out to the limit as a approaches 3 from the left(+) of (1/9 ln 1/4 - 1/9 ln |(a-3)/(a+3)|) + limit as b approaches infinity from the right (-) of (1/9 ln |(b-3)/(b+3)| - 1/9 ln 1/4) How do you solve that?

Also I can't figure out that the limit of e^(-1/x) as x approaches 0 from the right and from the left is.

Finially I don't know where to even start on the integral of

sqrt(9-(lnx)^2)

(lnx^x)