Question Number 73565 by Rio Michael last updated on 13/Nov/19
$${investigate}\:{the}\:{continuity}\:{of}\:{f}\:,{given}\:{by} \\ $$ $${f}:\:{x}\:\rightarrow\:\begin{cases}{\mathrm{1}−{x},\:{if}\:{x}<\mathrm{1}}\\{\mathrm{0},{if}\:{x}\:=\mathrm{1}}\\{{x}^{\mathrm{2}} −\mathrm{3}{x}\:+\:\mathrm{2},{if}\:{x}\:>\mathrm{1}}\end{cases} \\ $$ $${at}\:{the}\:{point}\:{x}\:=\mathrm{1} \\ $$ $$ \\ $$
Commented byRio Michael last updated on 13/Nov/19
$${thanks}\:{sir} \\ $$
Commented bykaivan.ahmadi last updated on 13/Nov/19
$${lim}_{{x}\rightarrow\mathrm{1}^{−} } {f}\left({x}\right)={lim}_{{x}\rightarrow\mathrm{1}^{−} } \left(\mathrm{1}−{x}\right)=\mathrm{0} \\ $$ $${lim}_{{x}\rightarrow\mathrm{1}^{+} } {f}\left({x}\right)={lim}_{{x}\rightarrow\mathrm{1}^{+} } \left({x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}\right)=\mathrm{0} \\ $$ $${f}\left(\mathrm{1}\right)=\mathrm{0} \\ $$ $${f}\:{is}\:{continuous}\:{at}\:{x}=\mathrm{1}. \\ $$ $$ \\ $$