91Ó°ÊÓ

For a certain speaker of the vowel in the word hot, \(A_{m}=7 A_{t}, L_{m}=8 \mathrm{~cm}\), and \(L_{t}=9 \mathrm{~cm} .\) Using the two-tube model, find the first three natural frequencies of the vocal tract.

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 \((-\infty, \infty)\). $$ f(x)=\frac{1}{3} x^{3}-\frac{1}{2} x^{2}-2 x+1 $$

Find the limit, if it exists. $$ \lim _{x \rightarrow-2} \frac{x^{3}+8}{x^{2}-4} $$

Find the limit, if it exists. $$ \lim _{x \rightarrow \infty} \frac{-6 x^{3}+7 x}{2 x^{2}-3 x-10} $$

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 \((-\infty, \infty)\). $$ f(x)=x^{4}-2 x^{2} $$

Find the limit, if it exists. $$ \lim _{x \rightarrow-\infty} \frac{-6 x^{3}+7 x}{2 x^{2}-3 x-10} $$

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 \((-\infty, \infty)\). $$ f(x)=2 x^{4}-4 x^{2}+2 $$

Find the limit, if it exists. $$ \lim _{x \rightarrow 1} \frac{x^{3}-1}{x^{2}-1} $$

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 \((-\infty, \infty)\). $$ f(x)=\tan x+\cot x, \quad(0, \pi / 2) $$

Find the limit, if it exists. $$ \lim _{x \rightarrow-\infty} \frac{7 x^{5}+x-9}{6 x+x^{3}} $$