Question

qual o limite de {(x-1)/raiz quadrada (x^2+1)] quando x tende a -infinito?

Answer 1

Olá, Rayana.

 

$<var>\lim_{x \to \infty}\frac{x-1}{\sqrt{x^2+1}}=\lim_{x \to \infty}\frac{x-1}{\sqrt{x^2(1+\frac{1}{x^2})}}=\lim_{x \to \infty}\frac{x-1}{x\sqrt{1+\frac{1}{x^2}}}=</var>$

 

$<var>\lim_{x \to \infty}\frac{x}{x\sqrt{1+\frac{1}{x^2}}}-\underbrace{\lim_{x \to \infty}\frac{1}{x\sqrt{1+\frac{1}{x^2}}}}_{=0}=\lim_{x \to \infty}\frac{1}{\sqrt{1+\frac{1}{x^2}}}=</var>$

 

$<var>=\frac{1}{\sqrt{1+0}}=\frac11=1</var>$