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**Jhevon** did you mean $\displaystyle \lim_{T \to \infty} \frac {T^2 + 2}{T^3 + T^2 - 1}$? if so, you are correct

i suppose you mean $\displaystyle y = \frac {1 + x^4}{x^2 - x^4}$ (you should use parentheses).

your horizontal asymptote is fine. as for you vertical asymptotes, what about x = 0?

your vertical asymptote is wrong. remember, you want $\displaystyle e^x - 5 = 0$

for the horizontal, you forgot y = 2. remember you have to take two infinite limits here, $\displaystyle \lim_{x \to \infty}f(x)$ and $\displaystyle \lim_{x \to - \infty}f(x)$

correct, it "oscillates"