Hey skg94.
For the second one, something is a limit if the limit exists from both sides with the same value. I think this should be a limit as well (does your question ask about 1/(x-3) instead?)
(x^2+16x+64)/(x+8)
So i factored and simplified to (x+8) from the left its negative infinity and the right positive infinity right? My textbook says its a limit with a value of 0 (lim x --> -8)
Also
lim x--> 3 = 1 / (x-3)^2 from both the left and right would be positive infinity if i understand limits right. My textbook says its not a limit.