Stumped on two problems:

1.

I haven't worked with limits in awhile, and I can't find any examples in my notes involving exponentials.

The second problem is:

2.

Rationalizing didnt work out very well, my preferred method would have been L Hopitals rule but we havent covered it in class yet so Im not sure if I can use that in my work.

Any help would be greatly appreciated! =)