Evaluate each limit$.$ Write the answer in the exact form. Show work for full marks.

a$.\underset{x}{lim}\frac{-x^2-7}{7x^2}=\frac{x^3(-3-\frac{7}{x^3})}{x^3(\frac{7}{x^3}1)}=\frac{-3-\frac{7}{x^2}}{1\frac{7}{x^3}}$

$[6$C$]$ as $x,\frac{7}{4\frac{1}{4}}0$

$\underset{x}{lim}\frac{-3-\frac{3}{x}}{1\frac{7}{x^3}}=\frac{-3-0}{10}=-3$

:$.$ as $x2,$ value of the expression approaches $-3$ b$)\underset{x\underset{?}{lim}}{lim}\frac{-2x^3-7}{7x^3}=-3$

b$.,\underset{x2}{lim}\frac{16-x^4}{x^2-8}$

c$.,\underset{x2}{lim}\frac{\sqrt[\phantom{2}]{6-x}-2}{\sqrt[\phantom{2}]{3-x}-1}$