Question

lim x➡a (x+2)^3÷2 - (a+2)^3÷2 / (x-a)​

Answer 1

Step-by-step explanation:[math]\Large \displaystyle \lim_{x \to a} \dfrac{\sqrt{(x+2)^3} - \sqrt{(a+2)^3}}{x-a}[/math]Use[math]\Large \boxed{(a+b)(a-b) = a^2 - b^2}[/math][math]\Large \boxed{a^3 - b^3 = (a-b)(a^2 + ab + b^2)}[/math]Then remove that factor.Time to solve, yeah, use the first identity[math]\displaystyle \lim_{x \to a} \dfrac{(x+2)^3 - (a+2)^3}{(x-a)(\sqrt{(x+2)^3} + \sqrt{(a+2)^3})}[/math][math]= \displaystyle \lim_{x \to a} \dfrac{(x-a)(x^2 + 4x + 4 + a^2 + 4a + 4 - ax - 2a - 2x - 4)}{(x-a)(\sqrt{(x+2)^3} + \sqrt{(a+2)^3})}[/math]

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