find the limt #2

$\begin{aligned} L & = \lim_{x \to \frac \pi 4} \frac {\sin x - \cos x}{\ln (\cot x)} & \small \blue{\text{A 0/0 case, L'Hôpital's rule applies.}} \\ & = \lim_{x \to \frac \pi 4} \frac {\cos x + \sin x}{-\tan x - \cot x} & \small \blue{\text{Differentiate up and down w.r.t. }x} \\ & = - \frac {\sqrt 2}2 \approx \boxed{-0.707} \end{aligned}$

Reference: L'Hôpital's rule

Transforming the variable from $x$ to $h=\frac{π}{4}-x$ and applying L'Hospital's rule we get the value of the limit as

$-\sqrt 2 \times \dfrac {1}{2}=-\dfrac {1}{\sqrt 2 }=\boxed {-0.7071}$ .