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Question Number 127295 by Dwaipayan Shikari last updated on 28/Dec/20 $$\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \frac{{tanh}^{−\mathrm{1}} {x}}{\:\sqrt[{\mathrm{5}}]{{x}}}{dx}\:\:\:\:\:\:\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 61755 by arcana last updated on 08/Jun/19 $$\mathrm{if}\:{f}\left({z}\right)=\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{a}_{{k}} {z}^{{k}} ,{a}_{{k}} ,{z}\in\mathbb{C}.\mathrm{Prove} \\ $$$$ \\ $$$${a}_{{k}} =\frac{\mathrm{1}}{\mathrm{2}\pi{i}}\underset{\mid{z}\mid={r}\:} {\int}\frac{{f}\left({z}\right)}{{z}^{{k}+\mathrm{1}} }{dz} \\ $$$$ \\…
Question Number 127293 by Dwaipayan Shikari last updated on 28/Dec/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{coth}\left({n}\right)}{{n}^{\mathrm{3}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 61744 by Cheyboy last updated on 08/Jun/19 $$\mathrm{3}{xy}^{\mathrm{2}} +{x}^{\mathrm{3}} =\mathrm{9}\:−−−−−\left(\mathrm{1}\right) \\ $$$$\mathrm{3}{x}^{\mathrm{2}} {y}+{y}^{\mathrm{3}} =\mathrm{18}−−−−\left(\mathrm{2}\right) \\ $$$${Find}\:{x}\:{and}\:{y} \\ $$ Commented by Cheyboy last updated…
Question Number 192791 by Mastermind last updated on 27/May/23 $$\mathrm{If}\:\mathrm{n}\:\mathrm{is}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{integer},\:\mathrm{prove}\:\mathrm{that}\: \\ $$$$\mathrm{2}^{\mathrm{n}} \Gamma\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}}\right)\:=\:\mathrm{1}.\mathrm{3}.\mathrm{5}…\left(\mathrm{2n}−\mathrm{1}\right)\sqrt{\pi}. \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$ Answered by Mathspace last updated on…
Question Number 192746 by Mastermind last updated on 26/May/23 $$\mathrm{Let}\:\mathrm{G}\:\mathrm{be}\:\mathrm{the}\:\mathrm{group}\:\left(\left\{\mathrm{1},\:\imath,\:−\mathrm{1},\:−\imath\right\},\:\centerdot\right) \\ $$$$\mathrm{and}\:\mathrm{let}\:\mathrm{H}\:\leqslant\:\left(\underset{−} {+}\mathrm{1},\:\centerdot\right),\:\mathrm{show}\:\mathrm{that} \\ $$$$\theta:\mathrm{G}\rightarrow\mathrm{H}\:\mathrm{is}\:\mathrm{an}\:\mathrm{Isomorphism}. \\ $$$$ \\ $$$$\mathrm{Hello}! \\ $$ Answered by aleks041103 last…
Question Number 192737 by Mastermind last updated on 25/May/23 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sequence}\:\left\{\mathrm{a}_{\mathrm{n}} \right\}\:\mathrm{is}\:\mathrm{null} \\ $$$$\mathrm{when}\:\left\{\mathrm{a}_{\mathrm{n}} \right\}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:\frac{\mathrm{n}^{\mathrm{3}} +\mathrm{2n}^{\mathrm{2}} −\mathrm{1}}{\mathrm{n}^{\mathrm{4}} −\mathrm{n}^{\mathrm{2}} +\mathrm{2}} \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$ Answered…
Question Number 192738 by Mastermind last updated on 25/May/23 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{supremum}\:\mathrm{and}\:\mathrm{infimum} \\ $$$$\mathrm{of}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{sequence} \\ $$$$ \\ $$$$\left.\mathrm{a}\left.\right)\left.\:\left\{\frac{\mathrm{n}−\mathrm{1}}{\mathrm{2n}}\right\}\:\:\:\:\mathrm{b}\right)\:\left\{\frac{\left(−\right)^{\mathrm{n}} \mathrm{n}}{\mathrm{2n}+\mathrm{1}}\right\}\:\:\:\:\mathrm{c}\right)\left\{\frac{\mathrm{1}+\left(−\right)^{\mathrm{n}} }{\mathrm{3}}\right\} \\ $$$$ \\ $$$$\left.\mathrm{d}\left.\right)\:\left\{\mathrm{sin}\frac{\mathrm{n}\pi}{\mathrm{2}}\right\}\:\:\:\:\mathrm{e}\right)\:\left\{\frac{\mathrm{1}}{\mathrm{n}}\:−\:\mathrm{sin}\frac{\mathrm{n}\pi}{\mathrm{2}}\right\} \\ $$$$ \\…