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

Question Number 184883 by mathlove last updated on 13/Jan/23

\lim_{x \to 2} \frac{\sqrt{x - 2}}{x - 2} = ?

Answered by aba last updated on 13/Jan/23

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

Commented by Frix last updated on 13/Jan/23

\lim_{x \to 2} f (x) is not the same as \lim_{x \to 2^{+}} f (x) if

\lim_{x \to 2^{-}} f (x) {doesn}^{'} t exist .

\lim_{x \to 2} f (x) {doesn}^{'} t exist if \lim_{x \to 2^{-}} f (x) \neq \lim_{x \to 2^{+}} f (x)

Commented by aba last updated on 13/Jan/23

the function is undefined on the left side

Commented by Frix last updated on 13/Jan/23

Yes . This means, the limit {doesn}^{'} t exist .

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