What's the limit of $\frac{1}{x - 1} arctan (\frac{2}{x - 1} - \frac{π}{2})$ $1/(x-1)arctan(2/(x-1)-pi/2)$ as x approaches positive 1 ? Thanks!

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Answer 1 · 2016-11-23T12:28:58

$\infty$ $oo$

$lim_(x->1)arctan(a/(x-1)+b)$ with $a > 0$ is $pi/2$ so

$lim_(x->1)1/(x-1)arctan(2/(x-1)-pi/2) = lim_(x->1)1/(x-1)lim_(x->1)arctan(2/(x-1)-pi/2) = oo xx pi/2= oo$

What's the limit of 1/(x-1)arctan(2/(x-1)-pi/2)1x−1arctan(2x−1−π2)1/(x-1)arctan(2/(x-1)-pi/2) as x approaches positive 1 ? Thanks!