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lim-0-1-e-ncos-x-dx-

Question Number 207723 by SANOGO last updated on 24/May/24 $$\mathrm{li}{m}\int_{\mathrm{0}} ^{\infty} \left(\mathrm{1}−{e}^{−{ncos}\left({x}\right)} \right){dx} \\ $$ Commented by Frix last updated on 24/May/24 $${f}\left({x}\right)=\mathrm{1}−\mathrm{e}^{−{n}\mathrm{cos}\:{x}} \\ $$$${n}\rightarrow\infty\:\Rightarrow\:{f}\left({x}\right)=\begin{cases}{\mathrm{1};\:−\frac{\pi}{\mathrm{2}}+{k}\pi\leqslant{x}\leqslant\frac{\pi}{\mathrm{2}}+{k}\pi}\\{−\infty;\:\frac{\pi}{\mathrm{2}}+{k}\pi<{x}<\frac{\mathrm{3}\pi}{\mathrm{2}}+{k}\pi}\end{cases}\forall{k}\in\mathbb{Z}…

f-n-x-n-1-x-2-sin-x-n-x-0-1-n-1-calculer-lim-n-0-1-f-n-x-dx-

Question Number 207648 by SANOGO last updated on 22/May/24 $${f}_{{n}} \left({x}\right)=\frac{{n}}{\mathrm{1}+{x}^{\mathrm{2}} }{sin}\left(\frac{{x}}{{n}}\right)\:\:/{x}\in\left[\mathrm{0},\mathrm{1}\right]\:,\:\:{n}\geqslant\mathrm{1} \\ $$$${calculer}\:{lim}\:{n}\rightarrow\infty\int_{\mathrm{0}} ^{\mathrm{1}} {f}_{{n}} \left({x}\right){dx} \\ $$ Commented by mr W last updated…

we-have-100-money-if-we-want-to-buy-100-Donkys-Horses-and-Camels-mixed-while-20-Donkys-cost-1-money-1-Horse-costs-1-money-and-1-Camel-costs-5-money-find-total-number-of-Donkys-Horses-and-Camels-

Question Number 207610 by Davidtim last updated on 20/May/24 $${we}\:{have}\:\mathrm{100}\:{money}\:{if}\:{we}\:{want}\:{to}\:{buy}\:\mathrm{100}\:{Donkys}\:{Horses} \\ $$$${and}\:{Camels}\:{mixed}\:{while}\:\mathrm{20}\:{Donkys} \\ $$$${cost}\:\mathrm{1}\:{money},\:\mathrm{1}\:{Horse}\:{costs}\:\mathrm{1}\:{money}\:{and} \\ $$$$\mathrm{1}\:{Camel}\:{costs}\:\mathrm{5}\:{money}. \\ $$$${find}\:{total}\:{number}\:{of}\:{Donkys},\:{Horses}, \\ $$$${and}\:{Camels}. \\ $$ Commented by Davidtim…

lim-oo-1-oo-x-n-1-x-n-2-dx-

Question Number 207547 by SANOGO last updated on 18/May/24 $${lim}\rightarrow+{oo}\:\int_{\mathrm{1}} ^{+{oo}} \:\frac{{x}^{{n}} }{\mathrm{1}+{x}^{{n}+\mathrm{2}} }{dx}\:=? \\ $$ Commented by SWPlaysMC last updated on 18/May/24 $$\mathrm{Just}\:\mathrm{so}\:\mathrm{you}\:\mathrm{know},\:\mathrm{the}\:\mathrm{infinity}\:\mathrm{symbol}\:\mathrm{is}\:\infty\:\mathrm{and}\:\mathrm{not}\:“{oo}'' \\…