Question Number 128731 by TITA last updated on 09/Jan/21 $$\mathrm{for}\:\:\mathrm{a}>\mathrm{b}>\mathrm{0}\:\:\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{b}<\frac{\mathrm{ax}^{\mathrm{x}} +\mathrm{bx}^{−\mathrm{x}} }{\mathrm{e}^{\mathrm{x}} +\mathrm{e}^{−\mathrm{x}} }<\mathrm{a} \\ $$ Commented by TITA last updated on 09/Jan/21…
Question Number 128725 by Dwaipayan Shikari last updated on 09/Jan/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{coth}\left({n}\pi\right)}{{n}^{\mathrm{4}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128566 by Dwaipayan Shikari last updated on 08/Jan/21 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2}}.\frac{\mathrm{1}}{\mathrm{1}!}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{3}}\left(\frac{\mathrm{1}.\mathrm{3}}{\mathrm{2}^{\mathrm{2}} }.\frac{\mathrm{1}}{\mathrm{2}!}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{4}}\left(\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}}{\mathrm{2}^{\mathrm{3}} }.\frac{\mathrm{1}}{\mathrm{3}!}\right)^{\mathrm{2}} +…=_{\mathrm{2}} {F}_{\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{2}};\mathrm{2};\mathrm{1}\right)=\frac{\mathrm{4}}{\pi} \\ $$ Commented by Dwaipayan Shikari last…
Question Number 128561 by 777316 last updated on 08/Jan/21 Answered by Dwaipayan Shikari last updated on 08/Jan/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{cosx}+\left(\frac{\mathrm{1}−{cosx}}{{sinx}}\right)=\mathrm{1}+\frac{\mathrm{2}{sin}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{{sinx}}=\mathrm{1} \\ $$ Terms of Service…
Question Number 128557 by AgnibhoMukhopadhyay last updated on 08/Jan/21 $$\: \: \: \: \: \: \: \: \: \\ $$$$\: \: \: \\ $$ Answered…
Question Number 128522 by BHOOPENDRA last updated on 08/Jan/21 $${f}\left({t}\right)={t}+\mathrm{1}\:\:\:\:\:\:\mathrm{0}\leqslant{t}\leqslant\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=\mathrm{3}\:\:\:\:\:\:\:\:\:\:{t}>\mathrm{2} \\ $$$${find}\:{laplace}\:{transformation}? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128485 by BHOOPENDRA last updated on 07/Jan/21 $${f}\left({t}\right)=\frac{\mathrm{1}−{cos}\mathrm{2}{t}}{{t}} \\ $$$${find}\:{laplace}\:{transformation}? \\ $$ Answered by Dwaipayan Shikari last updated on 07/Jan/21 $$\mathscr{L}\left(\frac{\mathrm{1}−{cos}\mathrm{2}{t}}{{t}}\right)\Rightarrow{I}\left({s}\right)=\int_{\mathrm{0}} ^{\infty} {e}^{−{st}}…
Question Number 128460 by BHOOPENDRA last updated on 07/Jan/21 $$\mathrm{2}{e}^{\mathrm{3}{t}} {sin}\mathrm{4}{t}\: \\ $$$${find}\:{laplace}\:{transformation}? \\ $$ Answered by Dwaipayan Shikari last updated on 07/Jan/21 $$\mathscr{L}\left(\mathrm{2}{e}^{\mathrm{3}{t}} {sin}\mathrm{4}{t}\right)…
Question Number 128445 by BHOOPENDRA last updated on 07/Jan/21 $${tsinh}\mathrm{2}{t}\:{sin}\mathrm{3}{t}\: \\ $$$${find}\:{the}\:{laplace}\:{transformation}? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 62907 by aliesam last updated on 26/Jun/19 $$\int\sqrt{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\:}\left(\mathrm{1}+{x}\right)\:{dx} \\ $$ Commented by mathmax by abdo last updated on 26/Jun/19 $${let}\:{A}\:=\int\sqrt{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}}\left(\mathrm{1}+{x}\right){dx}\:{changement}\:{x}\:={cos}\left(\mathrm{2}\theta\right)\:{give}\:\mathrm{2}\theta\:={arcosx}\:\Rightarrow \\ $$$${A}\:=\int\:\sqrt{\frac{\mathrm{2}{cos}^{\mathrm{2}} \left(\theta\right)}{\mathrm{2}{sin}^{\mathrm{2}}…