Question Number 107679 by seedhamaieng@gmail.com last updated on 12/Aug/20 $$\mathrm{dear}\:\mathrm{tinku}\:\mathrm{tara}\: \\ $$$$\mathrm{Please}\:\mathrm{add}\:\mathrm{a}\:\mathrm{option}\:\mathrm{which}\:\mathrm{gives}\: \\ $$$$\mathrm{us}\:\mathrm{to}\:\mathrm{save}\:\mathrm{a}\:\mathrm{file}\:\mathrm{as}\:\mathrm{pdf}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 173188 by dragan91 last updated on 08/Jul/22 Answered by mr W last updated on 08/Jul/22 $${t}=\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}\:>\mathrm{0} \\ $$$$\frac{\mathrm{2}{t}}{\:\sqrt{{t}^{\mathrm{2}} +\mathrm{1}}}+\frac{\mathrm{2}\left({t}^{\mathrm{2}} +\mathrm{1}\right)}{{t}}=\mathrm{4}+\sqrt{\mathrm{2}} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\frac{\mathrm{1}}{{t}}}}+{t}+\frac{\mathrm{1}}{{t}}=\mathrm{2}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}…
Question Number 107654 by mathdave last updated on 12/Aug/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 107639 by mathdave last updated on 11/Aug/20 Answered by mathmax by abdo last updated on 12/Aug/20 $$\mathrm{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{xln}\left(\mathrm{x}\right)}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{2}} }\mathrm{dx}\:\:\mathrm{we}\:\mathrm{have}\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{x}}\:=\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \left(−\mathrm{1}\right)^{\mathrm{n}} \:\mathrm{x}^{\mathrm{n}}…
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Question Number 107638 by mathdave last updated on 11/Aug/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 173164 by SANOGO last updated on 07/Jul/22 Answered by CElcedricjunior last updated on 08/Jul/22 $$\boldsymbol{\mathrm{det}}\left(\boldsymbol{\mathrm{M}}\right)=\mathrm{0}−\boldsymbol{\mathrm{a}}\left(\mathrm{1}+\boldsymbol{\mathrm{a}}^{\mathrm{2}} \right)+\boldsymbol{\mathrm{a}}^{\mathrm{2}} \left(\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{a}}^{\mathrm{3}} \right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\boldsymbol{\mathrm{a}}\left(\boldsymbol{\mathrm{a}}^{\mathrm{4}} −\mathrm{1}\right) \\ $$$$\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{M}}\:\boldsymbol{\mathrm{inversible}}\:\boldsymbol{\mathrm{if}}…
Question Number 107618 by mathdave last updated on 11/Aug/20 Answered by hgrocks last updated on 11/Aug/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 107621 by mathdave last updated on 11/Aug/20 Commented by john santu last updated on 12/Aug/20 $$\Gamma\left(\mathrm{2}{x}\right)\:=\:\frac{\mathrm{4}^{{x}} \:\Gamma\left({x}\right)\:\Gamma\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)}{\mathrm{2}\sqrt{\pi}}\:.\: \\ $$$${put}\:{x}\:=\:\frac{{n}}{\mathrm{4}} \\ $$$$\Gamma\left(\frac{{n}}{\mathrm{2}}\right)\:=\:\frac{\mathrm{4}^{\frac{{n}}{\mathrm{4}}} \Gamma\left(\frac{{n}}{\mathrm{4}}\right)\Gamma\left(\frac{{n}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{2}}\right)}{\mathrm{2}\sqrt{\pi}}\: \\…