Question Number 146528 by 0731619 last updated on 13/Jul/21
Answered by Olaf_Thorendsen last updated on 14/Jul/21
$$\mathrm{Let}\:{x}\:=\:\mathrm{6}+\epsilon \\ $$$$\frac{{x}!!−\mathrm{48}}{\mathrm{6}−\sqrt{\mathrm{6}{x}}}\:=\:\frac{\left(\mathrm{6}+\epsilon\right)\left(\mathrm{4}+\epsilon\right)\left(\mathrm{2}+\epsilon\right)−\mathrm{48}}{\mathrm{6}−\sqrt{\mathrm{6}\left(\mathrm{6}+\epsilon\right)}} \\ $$$$=\:\frac{\mathrm{44}\epsilon+\mathrm{12}\epsilon^{\mathrm{2}} +\epsilon^{\mathrm{3}} }{\mathrm{6}−\mathrm{6}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}.\frac{\epsilon}{\mathrm{6}}\right)}\:\underset{\epsilon\rightarrow\mathrm{0}} {\sim}\:−\mathrm{88} \\ $$