Hello. I'm new here, however, I think that I can help you. The answers to your questions are 1) DNE (infinity) and 2) 0.
Neither of these functions are defined on the other side of the limiting value, so you are forced to analyze the limits from only one side. This is fine. After all, one-sided limits are defined along the same criteria as two-sided limits. Without going into a formal epsilon-delta definition, a limit exists if there is convergence as you near the limiting value. That is, if a function grows excessively large, excessively small, or continually oscillates between values as you approach the limiting value, its limit at that limiting value does not exist.
The first function's limit is infinity because as you approach 3 the function grows without bound. The second function's limit is 0 because that is where the function converges as T approaches 0. The first conclusion was reached through simple direct substitution. The second function is a bit trickier because you need to remove a one-sided discontinuity through rationalization.