lim-x-1-x-1-x-2-1-

Question Number 111100 by bobhans last updated on 02/Sep/20

\lim_{x \to 1^{+}} \frac{x - 1}{\sqrt{x^{2} - 1}} ?

Answered by 1549442205PVT last updated on 02/Sep/20

\lim_{x \to 1^{+}} \frac{x - 1}{\sqrt{x^{2} - 1}} = \lim_{x \to 1^{+}} \frac{x - 1}{\sqrt{(x - 1) (x + 1}}

= \lim_{x \to 1^{+}} \frac{\sqrt{x - 1}}{\sqrt{x + 1}} = \frac{0}{\sqrt{2}} = 0

Answered by Rio Michael last updated on 02/Sep/20

\frac{x - 1}{\sqrt{x^{2} - 1}} \times \frac{\sqrt{x^{2} - 1}}{\sqrt{x^{2} - 1}} = \frac{(x - 1) (\sqrt{x^{2} - 1})}{x^{2} - 1} = \frac{\sqrt{x^{2} - 1}}{x + 1}

x \to 1^{+} \Rightarrow \frac{\sqrt{x^{2} - 1}}{x + 1} \to 0