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Author: Tinku Tara

lim-x-lnx-x-lnx-x-

Question Number 72495 by Tony Lin last updated on 29/Oct/19 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{{lnx}}{{x}}\right)^{\frac{{lnx}}{{x}}} =? \\ $$ Commented by mathmax by abdo last updated on 29/Oct/19 $${let}\:{f}\left({x}\right)=\left(\frac{{lnx}}{{x}}\right)^{\frac{{lnx}}{{x}}}…

nice-calculus-n-1-n-2-n-4-n-

Question Number 138026 by mnjuly1970 last updated on 09/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:………{nice}\:\:…\:…\:…\:{calculus}……….. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\Theta=\:\underset{\overset{{n}=\mathrm{1}} {\:}} {\overset{\infty} {\sum}}\left(\frac{{n}^{\mathrm{2}} }{{n}!.\mathrm{4}^{{n}} }\right)\:=?? \\ $$ Answered by Dwaipayan Shikari last updated…