Consider the function \( f(x)=\frac{2 x^{4}+4 x^{3}-16 x^{2}}{x^{4}-20 x^{2}+64} \) a. Evaluate \( \lim _{x \rightarrow \infty} f(x) \) and \( \lim _{x \rightarrow-\infty} f(x) \), and then identify the horizontal asymptotes. b. Find the vertical asymptotes. For each asymptote \( x=a \), evaluate \( \lim _{x \rightarrow a^{-}} f(x) \) and \( \lim _{x \rightarrow a^{+}} f(x) \).

1) \( \int_{8}^{\frac{\text { III }}{\frac{\pi}{2}}} x \cdot c \)

Integrate as indicated. Assume \( \mathrm{g}(\mathrm{x})>0 \) whenever \( \ln g(\mathrm{x}) \) is involved. \( \int \frac{8 \mathrm{x}}{4 \mathrm{x}^{2}+1} \mathrm{dx} \) \( \int \frac{8 \mathrm{x}}{4 \mathrm{x}^{2}+1} \mathrm{dx}= \)

\( \int \frac { 3 / \sqrt { a ^ { 3 } y ^ { 4 } } x d x } { 4 / 3 a ^ { 2 } b ^ { 3 } x ^ { 2 } + 6 } \)

7.- Resuelve el siguiente límite * \( \operatorname{lí}_{t \rightarrow 1}\left(\frac{t^{2}+2 t+1}{2 t-4}\right) \) 2 -3 -2 3

1. \( \lim _{x \rightarrow \infty}(\overline{3 x-5}) \) 2. \( \lim _{x \rightarrow 0}(1-\tan x)^{\frac{4 x}{\sin ^{2} 3 x}} \)