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Author: Tinku Tara

Question-193323

Question Number 193323 by fit last updated on 10/Jun/23 Answered by MM42 last updated on 10/Jun/23 $$\left.\mathrm{9}\right)\:{n}\left({s}\right)=\mathrm{80}\:\&\:{n}\left({m}\right)=\mathrm{40}\:\&\:{n}\left({e}\right)=\mathrm{65} \\ $$$${n}\left({s}\right)={n}\left({m}\right)+{n}\left({e}\right)−{n}\left({m}\cap{e}\right) \\ $$$$\mathrm{80}=\mathrm{40}+\mathrm{65}−{n}\left({m}\cap{e}\right)\Rightarrow{n}\left({m}\cap{e}\right)=\mathrm{15} \\ $$$$\left.\mathrm{10}\right)\frac{\mathrm{15}!}{\mathrm{3}!\mathrm{2}!\mathrm{2}!\mathrm{2}!\mathrm{2}!\mathrm{2}!} \\ $$$$\left.\mathrm{11}\right)\mathrm{10}×\mathrm{9}×\mathrm{8}×\mathrm{7}…

Question-193268

Question Number 193268 by 073 last updated on 09/Jun/23 Answered by qaz last updated on 09/Jun/23 $$\left(\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−{x}\right)^{{n}} }{{n}!}\right)\left(\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−{x}\right)^{{n}} {x}}{{n}!\left({n}+\mathrm{1}\right)}\right)={xe}^{−{x}} \underset{{n}=\mathrm{0}} {\overset{\infty}…

Question-193267

Question Number 193267 by Mingma last updated on 09/Jun/23 Answered by cortano12 last updated on 09/Jun/23 $$\:\:\left(\mathrm{i}\right)\:\mathrm{4f}\left(\mathrm{x}\right)+\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)=\mathrm{24x}+\mathrm{5}+\frac{\mathrm{6}}{\mathrm{x}} \\ $$$$\:\:\left(\mathrm{ii}\right)\:\mathrm{4f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)+\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{24}}{\mathrm{x}}+\mathrm{5}+\mathrm{6x} \\ $$$$\:\:\left(\mathrm{i}\right)×\mathrm{4}=\:\mathrm{4f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)+\mathrm{16f}\left(\mathrm{x}\right)=\mathrm{96x}+\mathrm{20}+\frac{\mathrm{24}}{\mathrm{x}} \\ $$$$\:\:\left(\mathrm{i}\right)−\left(\mathrm{ii}\right) \\ $$$$\:\:\:\Rightarrow\mathrm{15f}\left(\mathrm{x}\right)=\mathrm{90x}+\mathrm{15}…

IS-THIS-RIGHT-I-0-e-ix-2-dx-I-2-0-e-ix-2-dx-0-e-iy-2-dy-0-0-e-iy-2-dye-ix-2-dx-0-0-e-i-x-2-y-2-dydx-dydx-dA-rdrd-I-2-0-pi-2-0-

Question Number 193316 by gatocomcirrose last updated on 10/Jun/23 $$ \\ $$$$\mathrm{IS}\:\mathrm{THIS}\:\mathrm{RIGHT}? \\ $$$$\mathrm{I}=\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\mathrm{ix}^{\mathrm{2}} } \mathrm{dx} \\ $$$$\mathrm{I}^{\mathrm{2}} =\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\mathrm{ix}^{\mathrm{2}} } \mathrm{dx}\int_{\mathrm{0}}…

a-b-c-gt-0-amp-a-2-b-2-c-2-3-prove-that-1-3-ab-bc-ca-a-b-c-2-1-3-1-a-b-1-b-c-1-c-a-

Question Number 193314 by York12 last updated on 10/Jun/23 $$ \\ $$$$\boldsymbol{{a}}\:,\boldsymbol{{b}},\:\boldsymbol{{c}}\:\:>\:\mathrm{0}\:\&\:\:\boldsymbol{{a}}^{\mathrm{2}} +\boldsymbol{{b}}^{\mathrm{2}} +\boldsymbol{{c}}^{\mathrm{2}} =\mathrm{3}\:\boldsymbol{{prove}}\:\boldsymbol{{that}}\: \\ $$$$\sqrt[{\mathrm{3}}]{\left(\mathrm{1}+\frac{\mathrm{3}}{\boldsymbol{{ab}}+\boldsymbol{{bc}}+\boldsymbol{{ca}}}\:\right)^{\left(\boldsymbol{{a}}+\boldsymbol{{b}}+\boldsymbol{{c}}\right)^{\mathrm{2}} } \:}\leqslant\left(\mathrm{1}+\frac{\boldsymbol{{a}}}{\boldsymbol{{b}}}\right)\left(\mathrm{1}+\frac{\boldsymbol{{b}}}{\boldsymbol{{c}}}\right)\left(\mathrm{1}+\frac{\boldsymbol{{c}}}{\boldsymbol{{a}}}\right) \\ $$ Answered by witcher3 last…