Evaluate the limit$,$ if it exists. $($If an answer does not exist, enter DNE.$)$

$\underset{h0}{lim}\frac{(h-8{)}^2-64}{h}$

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$7.[-/1$ Points$]$

SCALCET$92\mathrm{.}3\mathrm{.}024.$EP$.$

Consider the following limit$.$

$\underset{x2}{lim}\frac{2-x}{\sqrt[\phantom{2}]{x+2}-2}$

Simplify the rational expression as much as possible.

Evaluate the limit$,$ if it exists. $($If an answer does not exist, enter DNE.$)$

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$8.[-/1$ Points$]$

SCALCET$92\mathrm{.}3\mathrm{.}034.$

Evaluate the limit$,$ if it exists. $($If an answer does not exist, enter DNE.$)$

$\underset{h0}{lim}\frac{\frac{1}{(x+h{)}^2}-\frac{1}{x^2}}{h}$

$$

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$9.[-/1$ Points$]$

SCALCET$92\mathrm{.}3\mathrm{.}037.$

A graphing calculator is recommended.

Use the Squeeze Theorem to show that $\underset{x0}{lim}{x}^{2}cos(9x)=0.$

Illustrate by graphing the functions $f(x)=-x^2,g(x)=x^{2}cos(9x),$ and $h(x)=x^2$ on the same screen.

Let $f(x)=-x^2,g(x)=x^{2}cos(9x),$ and $h(x)=x^2.$ Then $?$hat$(v)cos(9x)$hat$(v)=>$hat$(v)x^{2}cos(9x)?$ hat$(v).$

Since $\underset{x0}{lim}f(x)=\underset{x0}{lim}h(x)=,$ by the Squeeze Theorem we have $\underset{x0}{lim}g(x)=$

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