lim-x-pi-6-2ln-sin-x-ln-pi-sec-x-1-

Question Number 154719 by liberty last updated on 21/Sep/21

\lim_{x \to \frac{π}{6}} \frac{2 \ln [Γ (\sin x)] - \ln π}{Γ (\sec x) - 1} = ?

Answered by john_santu last updated on 21/Sep/21

\lim_{x \to \frac{π}{6}} \frac{2 \cos x Ψ^{0} (\sin (x))}{2 \tan (2 x) \sec (2 x) Γ (\sec (2 x)) Ψ^{0} (\sec (2 x))} =

\frac{2 . \frac{\sqrt{3}}{2} . (- γ - \ln 4)}{2 . \sqrt{3} . 2.1 . (1 - γ)} = \frac{γ + \ln 4}{4 (γ - 1)}

γ = M a s c h e r a n i c o n s t a n t