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

Question Number 121074 by bramlexs22 last updated on 05/Nov/20

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

Answered by liberty last updated on 05/Nov/20

\lim_{x \to 1} \frac{x - 1}{\sqrt{(x - 1) (x + 1)}} = \lim_{x \to 1} \sqrt{\frac{x - 1}{x + 1}} = 0

Answered by liberty last updated on 05/Nov/20

L^{'} Hopital

\lim_{x \to 1} \frac{x - 1}{\sqrt{x^{2} - 1}} = \lim_{x \to 1} \frac{1}{[\frac{x}{\sqrt{x^{2} - 1}}]}

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

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