Question

Solve ${lim}_{x\to a}\{\frac{{(x+2)}^{5/3}-{(a+2)}^{5/3}}{x-a}\}$

Answer 1

Formula:

${lim}_{x\to a}\{\frac{x^n-a^n}{x-a}\}=a^{n-1}$

${lim}_{x\to a}\{\frac{(x+2{)}^{\frac{5}{3}}-(a+2{)}^{\frac{5}{3}}}{x-a}\}$

$={lim}_{x\to a}\{\frac{(x+2{)}^{\frac{5}{3}}-(a+2{)}^{\frac{5}{3}}}{(x+2)-(a+2)}\}$

$=(a+2{)}^{\frac{5}{3}-1}$

$=(a+2{)}^{\frac{2}{3}}$(Ans)