Evaluate each limit. 

lim x→0 cos x−1 / sin^2x

Evaluate each limit. 

lim x→0 e^4x−1 / e^x−1

Evaluate each limit. 

lim x→0+ 1−cos^2x / sin x

Evaluate each limit. 

lim x→e^2 ln^2x−5 ln x+6 lnx−2

Evaluate $\underset{x\to \infty }{\lim }f\left(x\right)$ and$\underset{x\to -\infty }{\lim }f\left(x\right)$.

$f\left(x\right)=\frac{4x^3+1}{1-x^3}$

Evaluate ${\(\displaystyle\[\lim\)_{x\(\to\]\infty\)}{f(x)}}$ and${\(\displaystyle\]\lim\)_{x\(\to\)-\(\infty\)}{f(x)}}$.

$f\left(x\right)=\frac{6e^x+20}{3e^x+4}$

Complete the following steps for the given functions. 

c. Graph $f$ and all of its asymptotes with a graphing utility. Then sketch a graph of the function by hand, correcting any errors appearing in the computer-generated graph.

$f\left(x\right)=\frac{x^2-3}{x+6}$

Complete the following steps for the given functions. 

c. Graph f and all of its asymptotes with a graphing utility. Then sketch a graph of the function by hand, correcting any errors appearing in the computer-generated graph.

$f\left(x\right)=\frac{4x^3+4x^2+7x+4}{x^2+1}$