Evaluate each limit. 

$\underset{x\to \pi }{\lim }\frac{{\cos }^2\left(x\right)+3\cos \left(x\right)+2}{{\cos }^{}\left(x\right)+1}$

Evaluate each limit. 

$\underset{x\to 3}{\lim }\sqrt{x^2+7}$

Evaluate each limit. 

$\underset{x\to \frac{\pi }{2}}{\lim }\frac{\sin \left(x\right)-1}{\sqrt{\sin \left(x\right)}-1}$

Find the horizontal asymptotes of each function using limits at infinity.

f(x) = (2e^x + 3) / (e^x + 1)

Determine the following limits.

lim x→∞ (2x − 3) / (4x + 10)

Determine the following limits.

lim x→∞ (x⁴ − 1) / (x⁵ + 2)

Determine the following limits.

lim x→∞ (3 tan^-1 x + 2)

Determine the following limits.

lim w→∞ (ln w²) / (ln w³ + 1)