Question

Solve ${lim}_{x\to 2}\left(\frac{x^5-32}{x^3-8}\right)$

Answer 1

Formula:

$li{m}_{x\to a}\frac{x^m-a^m}{x^n-a^n}=\frac{m}{n}(a{)}^{m-n}$

$li{m}_{x\to 2}\frac{x^5-32}{x^3-8}$

$=li{m}_{x\to 2}\frac{x^5-2^5}{x^3-2^3}$

$=\frac{5}{3}(2{)}^{5-3}$

$=\frac{5}{3}\times 4$

$=\frac{20}{3}$