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Category: Relation and Functions

1-let-n-Nand-A-n-0-pi-dx-1-cos-2-nx-calculate-A-n-2-f-C-0-0-pi-R-find-lim-n-0-pi-f-x-1-cos-2-nx-dx-

Question Number 32348 by abdo imad last updated on 23/Mar/18 $$\left.\mathrm{1}\right){let}\:{n}\:\in{Nand}\:\:\:{A}_{{n}} \:=\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{dx}}{\mathrm{1}+{cos}^{\mathrm{2}} \left({nx}\right)}\:.{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{f}\in\:{C}^{\mathrm{0}} \left(\left[\mathrm{0},\pi\right],\:{R}\right)\:{find}\:{lim}_{{n}\rightarrow\infty} \:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{f}\left({x}\right)}{\mathrm{1}+{cos}^{\mathrm{2}} \left({nx}\right)}{dx}\:. \\ $$ Terms…

let-t-0-and-f-t-t-1-t-prove-that-the-sequence-S-n-k-1-n-f-k-n-2-converges-and-find-its-limit-

Question Number 32335 by abdo imad last updated on 23/Mar/18 $${let}\:{t}\geqslant\mathrm{0}\:{and}\:{f}\left({t}\right)\:=\frac{{t}}{\:\sqrt{\mathrm{1}+{t}}}\:.{prove}\:{that}\:{the}\:{sequence} \\ $$$${S}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{f}\left(\frac{{k}}{{n}^{\mathrm{2}} }\right)\:\:{converges}\:{and}\:{find}\:{its}\:{limit}. \\ $$ Terms of Service Privacy Policy Contact:…

calculate-n-0-n-2-e-in-2-find-n-0-n-2-cos-n-and-n-0-n-2-sin-n-

Question Number 32300 by abdo imad last updated on 22/Mar/18 $${calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} {n}^{\mathrm{2}} \:{e}^{{in}\theta} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{n}^{\mathrm{2}} {cos}\left({n}\theta\right)\:{and}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{n}^{\mathrm{2}} {sin}\left({n}\theta\right)=. \\ $$ Terms…