Question

qual o limite de
${x}^{3} - 1 \div {x}^{2} - 1$
Quando x tende a 1

Answer 1

Vamos lá .

$\lim_{x \to \ 1} \frac{ x^{3} -1}{ x^{2} -1} _$ = $\lim_{x \to \ 1} \frac{(x-1).( x^{2} +x+1)}{(x-1).(x+1)} _$

$\lim_{x \to \ 1} \frac{ x^{3} -1}{ x^{2} -1} _$ = $\lim_{x \to \ 1} \frac{ x^{2} +x+1}{x+1} _$

$\lim_{x \to \ 1} \frac{ x^{3} -1}{ x^{2} -1} _$ = $\frac{ 1^{2}+1+1 }{1+1} = 3/2$