Answer
$\dfrac {1}{2}$
Work Step by Step
$\lim _{x\rightarrow 1}\dfrac {\arctan x-\pi /4}{x-1}=\dfrac {\dfrac {d}{dx}\left( \arctan x-\pi /4\right) }{\dfrac {d}{dx}\left( x-1\right) }=\dfrac {\dfrac {1}{1+x^{2}}}{1}=\dfrac {1}{1+x^{2}}=\dfrac {1}{2}$
