Calculate the limit:

A$.\underset{x0}{lim}\frac{x^2-25}{x^2-4x-5}$

B$.\underset{x-2}{lim}\frac{x^4+5x^3+6x^2}{x^2(x+1)-4(x+1)}$

C$.\underset{x2}{lim}\frac{x^2+2x-8}{\sqrt[\phantom{2}]{x^2+5}-(x+1)}$

D$.\underset{y5}{lim}(\frac{2y^2+2y+4}{6y-3}{)}^{\frac{1}{3}}$

E$.\underset{x{0}^{+}}{lim}\frac{e^x}{1+ln(x)}$

F$.\underset{x-}{lim}\sqrt[3]{\frac{x-3}{5-x}}$

G$.\underset{x}{lim}\frac{x+5}{2x^2+1}$

For the following functions, use the definition of a derivative to find $f^{\text{'}}(x).$

$f(x)=6$

$f(x)=\frac{2x}{7}+1$

$f(x)=\frac{3}{x}$

$f(x)=\sqrt[\phantom{2}]{x+4}$

Use the definition of the derivative to explain why $f^{\text{'}}(x)=-1\frac{1}{2x^{\frac{3}{2}}}$ if $f(x)=\frac{1}{\sqrt[\phantom{2}]{x}}$