Question

${lim}_{x\to 2}\frac{x^5-32}{x^3-8}=$

• A. $\frac{3}{20}$
• B. $\frac{20}{3}$
• C. $\frac{10}{3}$
• D. $\frac{3}{10}$

Answer 1

Answer: (B)

$\frac{20}{3}$

${lim}_{x\to 2}\frac{x^5-32}{x^3-8}$
$=\underset{x\to 2}{lim}\frac{x^5-32}{x-2}\underset{x\to 2}{lim}\frac{1}{\frac{x^3-8}{x-2}}$
$=\underset{x\to 2}{lim}\frac{x^5-2^5}{x-2}\underset{x\to 2}{lim}\frac{1}{\frac{x^3-2^3}{x-2}}$
$=5(2{)}^4\frac{1}{3(2{)}^2}$
$=\frac{20}{3}$