Calculus - Infinite Limits and Asymptotes (Several Problems)

Hi I just need help with several problems. I worked them out and I got an answer but I'm not sure if I did it correctly. Please check my answers.

**Problem 1**

Find the Limit:

Lim as X -> Positive Infinity of T^2 + 2/ T^3 + ^2 - 1

I don't want to put all my work because I don't know the shorthand to doing it and I'll just put the answer I got. I got 0 as the limit to this problem.

**Problem 2**

**Find the Horizontal and Vertical Asymptotes of each curve:**

Y = 1 + X^4/X^2-X^4

I got Horizontal = -1 and Vertical = 1, -1

**Problem 3**

Same as above

Y = 2e^x/e^x-5

I got Horizontal = 0 and Vertical = -1

**Problem 4**

Find the limit

Lim x-> positive infinity COSX

I got Lim doesn't exist because COSX is a periodic.