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calculer-lim-x-pi-n-1-sin-n-1-x-n-1-sin-n-1-x-sinx-sin-nx-

Question Number 195278 by Erico last updated on 28/Jul/23 $$\mathrm{calculer}\:\underset{\mathrm{x}\rightarrow\pi} {\mathrm{lim}}\frac{\left(\mathrm{n}+\mathrm{1}\right)\mathrm{sin}\left(\left(\mathrm{n}−\mathrm{1}\right)\mathrm{x}\right)−\left(\mathrm{n}−\mathrm{1}\right)\mathrm{sin}\left(\left(\mathrm{n}+\mathrm{1}\right)\mathrm{x}\right)}{\mathrm{sinx}\:\mathrm{sin}\left(\mathrm{nx}\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

In-1-e-lnx-n-x-2-dx-using-an-enclosing-lnx-on-interval-1-e-show-that-n-N-0-In-1-

Question Number 195223 by Rodier97 last updated on 27/Jul/23 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{In}=\int_{\mathrm{1}} ^{\mathrm{e}} \frac{\left({lnx}\right)^{{n}} }{{x}^{\mathrm{2}} }\:{dx} \\ $$$$\:\:\:\:\:\mathrm{using}\:\mathrm{an}\:\mathrm{enclosing}\:{lnx}\:\mathrm{on}\:\mathrm{interval}\:\left[\mathrm{1};\mathrm{e}\right]\:\mathrm{show}\:\mathrm{that}\:\forall{n}\:\in\:\mathbb{N}^{\ast} ,\:\mathrm{0}\:\leq\mathrm{In}\leq\:\mathrm{1} \\ $$$$ \\ $$$$ \\ $$$$…

Question-195206

Question Number 195206 by otchereabdullai@gmail.com last updated on 27/Jul/23 Answered by MM42 last updated on 27/Jul/23 $${p}\left({a}\right)={p}\left({b}\right)={p}\left({c}\right)=\frac{\mathrm{3}}{\mathrm{4}}\:;\:{probability}\:{of}\:{winning}\:{each}\:{race} \\ $$$$\left({i}\right)\:{p}\left({a}'\cap{b}\cap{c}'\right)=\frac{\mathrm{1}}{\mathrm{4}}×\frac{\mathrm{3}}{\mathrm{4}}×\frac{\mathrm{1}}{\mathrm{4}}=\frac{\mathrm{3}}{\mathrm{64}} \\ $$$$\left({ii}\right)\:{p}\left({a}\cap{b}\cap{c}\right)=\frac{\mathrm{27}}{\mathrm{64}} \\ $$$$\left({iii}\right)\:{p}\left(\Sigma{abc}'\right)=\mathrm{3}×\frac{\mathrm{1}}{\mathrm{4}}×\frac{\mathrm{9}}{\mathrm{16}}=\frac{\mathrm{27}}{\mathrm{64}} \\ $$…