Question Number 146529 by 0731619 last updated on 13/Jul/21
Answered by Olaf_Thorendsen last updated on 14/Jul/21
$$\mathrm{Let}\:{x}\:=\:\mathrm{5}+\epsilon \\ $$$$\frac{{x}!!!−\mathrm{10}}{{x}−\mathrm{5}}\:=\:\frac{\left(\mathrm{5}+\epsilon\right)\left(\mathrm{2}+\epsilon\right)−\mathrm{10}}{\mathrm{5}+\epsilon−\mathrm{5}} \\ $$$$=\:\frac{\mathrm{7}\epsilon+\epsilon^{\mathrm{2}} }{\epsilon}\:\underset{\epsilon\rightarrow\mathrm{0}} {\sim}\mathrm{7} \\ $$