91Ó°ÊÓ

Find the absolute maximum and minimum values of the function, if they exist, over the indicated interval. When no interval is specified, use the real line \((-\infty, \infty)\). $$ f(x)=\frac{\sin x}{1+\sin x} ; \quad(-\pi / 2,3 \pi / 2) $$

Find the limit, if it exists. $$ \lim _{x \rightarrow-\infty} \frac{2 x^{4}+x}{x+1} $$

Find the absolute maximum and minimum values of the function, if they exist, over the indicated interval. When no interval is specified, use the real line \((-\infty, \infty)\). $$ f(x)=\frac{1}{\sin x+\cos x} ; \quad(-\pi / 4,3 \pi / 4) $$

Find the absolute maximum and minimum values of the function, if they exist, over the indicated interval. When no interval is specified, use the real line \((-\infty, \infty)\). $$ f(x)=\frac{1}{x+2 \cos x} ; \quad[0, \pi] $$

Find the limit, if it exists. $$ \lim _{x \rightarrow \infty} \cos x $$

Find the absolute maximum and minimum values of the function, if they exist, over the indicated interval. When no interval is specified, use the real line \((-\infty, \infty)\). $$ f(x)=\frac{1}{x-2 \sin x} ;(0, \pi / 2) $$

Find the limit, if it exists. $$ \lim _{x \rightarrow \infty} \frac{\sin x}{x} $$

Find the absolute maximum and minimum values of the function, if they exist, over the indicated interval. When no interval is specified, use the real line \((-\infty, \infty)\). $$ f(x)=2 \csc x+\cot x, \quad(0, \pi) $$

Find the limit, if it exists. $$ \lim _{x \rightarrow \infty} \frac{\cos x}{x} $$

Find the absolute maximum and minimum values of the function, if they exist, over the indicated interval. When no interval is specified, use the real line \((-\infty, \infty)\). $$ f(x)=\tan x-2 \sec x, \quad(-\pi / 2, \pi / 2) $$