Question Number 73561 by Rio Michael last updated on 13/Nov/19
$${find}\:{the}\:{value}\:{of}\:\lambda\:{for}\:{which} \\ $$ $$\:{f}\::\:{x}\:\rightarrow\:\begin{cases}{\mathrm{2}\lambda\:−\:{x},\:{if}\:{x}\:<\:\mathrm{1}}\\{\lambda^{\mathrm{2}} \:+\:{x}\:−\mathrm{1},\:{if}\:{x}\:>\:\mathrm{1}}\end{cases} \\ $$ $${has}\:{a}\:{limit}\:{as}\:{x}\rightarrow\:\mathrm{1} \\ $$
Answered by ajfour last updated on 13/Nov/19
$$\mathrm{2}\lambda−\mathrm{1}=\lambda^{\mathrm{2}} \\ $$ $$\lambda=\mathrm{1}\:. \\ $$
Commented byRio Michael last updated on 13/Nov/19
$${thanks}\:{sir} \\ $$