use properties of limits to find the indicated limit. it may be necessary to rewrite an expression before…

Explanation:

Step1: Apply limit - sum/difference rule

$\lim_{x\rightarrow a}(f(x)\pm g(x)\pm h(x))=\lim_{x\rightarrow a}f(x)\pm\lim_{x\rightarrow a}g(x)\pm\lim_{x\rightarrow a}h(x)$. So, $\lim_{x\rightarrow 8}(x^{2}-3x - 2)=\lim_{x\rightarrow 8}x^{2}-\lim_{x\rightarrow 8}(3x)-\lim_{x\rightarrow 8}2$.

Step2: Apply limit - constant - multiple rule and power rule

For $\lim_{x\rightarrow 8}(3x)=3\lim_{x\rightarrow 8}x$ (constant - multiple rule) and $\lim_{x\rightarrow 8}x^{2}=8^{2}$ (power rule $\lim_{x\rightarrow a}x^{n}=a^{n}$). Also, $\lim_{x\rightarrow 8}2 = 2$ (limit of a constant). We know that $\lim_{x\rightarrow 8}x = 8$. So, $3\lim_{x\rightarrow 8}x=3\times8$.

Step3: Calculate the values

$\lim_{x\rightarrow 8}x^{2}=8^{2}=64$, $3\lim_{x\rightarrow 8}x = 24$, $\lim_{x\rightarrow 8}2 = 2$. Then $\lim_{x\rightarrow 8}(x^{2}-3x - 2)=64-24 - 2$.

Step4: Simplify the result

$64-24 - 2=38$.

Answer:

A. $\lim_{x\rightarrow 8}(x^{2}-3x - 2)=38$