Resposta :
Tem uma fatoração de a³ - b³. Ela é a³ - b³ = (a-b)(a² + ab + b²). Usando essa fatoração temos:
[tex]\lim\limits_{x \to 4} \frac{x^3 - 4^3}{x-4} = \lim\limits_{x \to 4} \frac{(x-4)(x^2 + 4x + 16)}{x-4}[/tex]
[tex]\lim\limits_{x \to 4} \frac{x^3 - 64}{x-4} = \lim\limits_{x \to 4}x^2 + 4x + 16[/tex]
[tex]\lim\limits_{x \to 4} \frac{x^3-64}{x-4} = 16 + 16 + 16[/tex]
[tex]\boxed{\boxed{\lim\limits_{x \to 4} \frac{x^3 - 64}{x-4} = 48}}[/tex]
[tex]\lim\limits_{x \to 4} \frac{x^3 - 4^3}{x-4} = \lim\limits_{x \to 4} \frac{(x-4)(x^2 + 4x + 16)}{x-4}[/tex]
[tex]\lim\limits_{x \to 4} \frac{x^3 - 64}{x-4} = \lim\limits_{x \to 4}x^2 + 4x + 16[/tex]
[tex]\lim\limits_{x \to 4} \frac{x^3-64}{x-4} = 16 + 16 + 16[/tex]
[tex]\boxed{\boxed{\lim\limits_{x \to 4} \frac{x^3 - 64}{x-4} = 48}}[/tex]