mathop {lim }limits_{x to a} frac{{{{(x + 2)} | vedclass

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Question

(A) We use the standard limit formula: $\mathop {\lim }\limits_{x 	o a} \frac{{x^n - a^n}}{{x - a}} = na^{n-1}$.Let $u = x + 2$. As $x 	o a$,$u 	o

Vedclass · Accepted Answer

$\frac{5}{3}{(a + 2)^{2/3}}$

Vedclass · Answer

(A) We use the standard limit formula: $\mathop {\lim }\limits_{x 	o a} \frac{{x^n - a^n}}{{x - a}} = na^{n-1}$.Let $u = x + 2$. As $x 	o a$,$u 	o a + 2$.The expression becomes $\mathop {\lim }\limits_{u 	o a+2} \frac{{u^{5/3} - (a+2)^{5/3}}}{{u - (a+2)}}$.Applying the formula with $n = 5/3$ and the variable $u$ approaching $a+2$,we get:$\frac{5}{3}(a+2)^{(5/3) - 1} = \frac{5}{3}(a+2)^{2/3}$.

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

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