Evaluate each limit. 


lim x→e^2 ln^2x−5 ln x+6 lnx−2

Evaluate each limit. 

lim θ→0 (1/(2+sinθ)-1/2)/sin θ

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

Determine the following limits.

$\underset{t\to \infty }{\lim }\frac{\cos \left(t\right)}{e^{3t}}$

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.

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