Question

O Limite de (x3 - 1)/(x -1), quando x tende a 1 é;

Grupo de escolhas da pergunta

( ) 3

( ) 1

( ) 0

( ) -1

( ) 2

Answer 1

Explicação passo-a-passo:

Temos que $f(x)=\dfrac{x^{3}-1 }{x-1}$

$\displaystyle\lim_{x \to \ 1} f(x)=\displaystyle\lim_{x \to \ 1}\frac{x^{3}-1 }{x-1}\\\\\text Fatorando\ o\ n\'umerador: \\\\\displaystyle\lim_{x \to \ 1} f(x)=\displaystyle\lim_{x \to \ 1}\frac{(x-1).(x^{2} +x.1+1^{2} ) }{x-1}\\\\\displaystyle\lim_{x \to \ 1} f(x)=\displaystyle\lim_{x \to \ 1}x^{2} +x+1\\\\\displaystyle\lim_{x \to \ 1} f(x)=1^{2}+1+1\\\\\boxed{\boxed{\displaystyle\lim_{x \to \ 1} f(x)=3}}$