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Author: Tinku Tara

let-f-x-ln-x-1-2-x-1-find-D-f-2-determine-f-1-3-calculate-f-x-dx-and-f-1-x-dx-

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Question Number 62129 by maxmathsup by imad last updated on 15/Jun/19 $${let}\:{f}\left({x}\right)={ln}\left({x}+\mathrm{1}−\mathrm{2}\sqrt{{x}}\right) \\ $$$$\left.\mathrm{1}\right)\:{find}\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{f}^{−\mathrm{1}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\:\int{f}\:\left({x}\right){dx}\:{and}\:\:\int\:{f}^{−\mathrm{1}} \left({x}\right){dx} \\ $$ Commented by arcana last…

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let-U-n-0-cos-nx-x-2-n-2-3-dx-with-n-1-1-calculate-U-n-intrems-of-n-2-find-lim-n-n-U-n-3-calculate-lim-n-n-2-U-n-4-study-the-convervence-of-U-n-

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Question Number 62128 by maxmathsup by imad last updated on 15/Jun/19 $${let}\:{U}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({nx}\right)}{\left({x}^{\mathrm{2}} \:+{n}^{\mathrm{2}} \right)^{\mathrm{3}} }{dx}\:\:{with}\:{n}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{intrems}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} {n}\:{U}_{{n}} \\…

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