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Question Number 153517 by liberty last updated on 08/Sep/21

  L=lim_(x→1) (((√(2019x−2018))−1)/( (x^(2019) )^(1/(2018)) −1))   then 2×L =?

$$\:\:{L}=\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\sqrt{\mathrm{2019}{x}−\mathrm{2018}}−\mathrm{1}}{\:\sqrt[{\mathrm{2018}}]{{x}^{\mathrm{2019}} }−\mathrm{1}} \\ $$$$\:{then}\:\mathrm{2}×{L}\:=? \\ $$

Commented by MJS_new last updated on 08/Sep/21

just “hospitalize” it ⇒ L=1009  [sorry I don′t know how to get 2L]

$$\mathrm{just}\:``\mathrm{hospitalize}''\:\mathrm{it}\:\Rightarrow\:{L}=\mathrm{1009} \\ $$$$\left[\mathrm{sorry}\:\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{how}\:\mathrm{to}\:\mathrm{get}\:\mathrm{2}{L}\right] \\ $$

Commented by liberty last updated on 08/Sep/21

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