Question Number 136741 by JulioCesar last updated on 25/Mar/21
Answered by Dwaipayan Shikari last updated on 25/Mar/21
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}!−\mathrm{1}}{{x}}=\frac{\Gamma\left({x}+\mathrm{1}\right)−\mathrm{1}}{{x}}=\frac{\Gamma'\left({x}+\mathrm{1}\right)}{\mathrm{1}}=\Gamma'\left(\mathrm{1}\right)=−\gamma \\ $$