Where-is-the-function-f-x-ln-x-tan-1-x-x-2-1-continous-

Question Number 130401 by john_santu last updated on 25/Jan/21

W h e r e i s t h e f u n c t i o n

f (x) = \frac{\ln x + \tan^{- 1} x}{x^{2} - 1} c o n t i n o u s ?

Answered by mathmax by abdo last updated on 25/Jan/21

f (x) = \frac{lnx + arctanx}{x^{2} - 1} f is defined on] 0, 1 [\cup] 1, + \infty [= D

f is contnue on D is f continue on 1 ?

\lim_{x \to 1^{+}} f (x) = \frac{\frac{π}{4}}{0^{+}} = + \infty and \lim_{x \to 1^{-}} f (x) = - \infty \Rightarrow f is not {onx}_{0} = 1