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find-the-value-of-for-which-f-x-2-x-if-x-lt-1-2-x-1-if-x-gt-1-has-a-limit-as-x-1-




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

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