Did i show this correct? calc III limits

Hello everyone, I don't seem to ever do well on these assignments, so i want to make sure I'm proving this right... Here is the question and my work, its 2 parts, but i'm going to make them into 2 seperate images so you can see it clearer.
Here is the first one:
http://img139.imageshack.us/img139/3374/vec1br.jpg
if that link is down or slow here is a mirror:
http://show.imagehosting.us/show/789..._-1_789730.jpg

Here is the second one:
http://img316.imageshack.us/img316/7677/vec26rg.jpg
mirror:
http://show.imagehosting.us/show/789..._-1_789797.jpg

THanks.