Question Number 73572 by Rio Michael last updated on 13/Nov/19
$${determine}\:{wether}\:{or}\:{not}\:{the}\:{function}\:{f},{where} \\ $$$${f}\left({x}\right)\:=\:\begin{cases}{\mathrm{2}{x}\:+\:\mathrm{1},\:\mathrm{0}\leqslant\:{x}\:<\mathrm{2}}\\{\mathrm{7}−{x},\:\:\:\mathrm{2}\:\leqslant\:{x}\:<\:\mathrm{4}}\\{\frac{\mathrm{3}{x}}{\mathrm{4}}\:,\:\:\mathrm{4}\:\leqslant\:{x}\:<\:\mathrm{6}}\end{cases} \\ $$$${is}\:{continuous}\:{in}\:{the}\:{interval}\:\left[\mathrm{0},\mathrm{6}\left[\right.\right. \\ $$
Commented by kaivan.ahmadi last updated on 13/Nov/19
$${lim}_{{x}\rightarrow\mathrm{2}^{−} } {f}\left({x}\right)={lim}_{{x}\rightarrow\mathrm{2}^{+} } {f}\left({x}\right)=\mathrm{5} \\ $$$${lim}_{{x}\rightarrow\mathrm{4}^{−} } {f}\left({x}\right)={lim}_{{x}\rightarrow\mathrm{4}^{+} } {f}\left({x}\right)=\mathrm{3} \\ $$$$\Rightarrow{f}\:{is}\:{continuous}. \\ $$