Question Number 219887 by SdC355 last updated on 03/May/25 $$\mathrm{what}\:\mathrm{is}\: \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)\uparrow\uparrow^{\infty} =?? \\ $$$${a}\uparrow\uparrow^{{m}} =\underset{{m}\:\mathrm{times}} {\underbrace{{a}^{{a}^{{a}^{{a}^{\iddots} } } } }}\:\:\left(\mathrm{aka}\:\mathrm{Knuth}'\mathrm{s}\:\mathrm{up}\:\mathrm{notation}\right) \\ $$ Answered…
Question Number 219872 by SdC355 last updated on 03/May/25 $$\mathrm{prove} \\ $$$$\int\:\:{Y}_{−\frac{\mathrm{3}}{\mathrm{2}}} \left({z}\right)\:\mathrm{d}{z}=\frac{\mathrm{4sin}\left({z}\right)+\frac{{z}\boldsymbol{\Gamma}\left(\frac{\mathrm{1}}{\mathrm{2}},−\boldsymbol{{i}}{z}\right)}{\:\sqrt{−\boldsymbol{{i}}{z}}}+\frac{{z}\boldsymbol{\Gamma}\left(\frac{\mathrm{1}}{\mathrm{2}},\boldsymbol{{i}}{z}\right)}{\:\sqrt{\boldsymbol{{i}}{z}}}}{\:\sqrt{\mathrm{2}\pi{z}}}+{C} \\ $$ Answered by MrGaster last updated on 03/May/25 $${Y}_{−\nu} =\left(−\mathrm{1}\right)^{\nu} {Y}_{\nu}…
Question Number 219870 by SdC355 last updated on 03/May/25 $$\int_{\mathrm{0}} ^{\:\infty} \:{K}_{\nu} \left({r}\right)\mathrm{d}{r} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:{t}\centerdot{Y}_{\mathrm{0}} \left({t}\right)\mathrm{d}{t} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:\:\frac{\mathrm{sin}\left({t}\right){e}^{−{kt}} }{{t}^{\mathrm{2}} +\rho^{\mathrm{2}} }\mathrm{d}{t}\:…
Question Number 219831 by SdC355 last updated on 02/May/25 $$\mathrm{prove} \\ $$$$\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{g}\left({z}+{h}\right)}{\mathrm{g}\left({z}\right)}\right)^{\frac{\mathrm{1}}{{h}}} ={e}^{\frac{\mathrm{d}\:\:}{\mathrm{d}{z}}\:\mathrm{ln}\:\left(\mathrm{g}\left({z}\right)\right)} ={e}^{\frac{\mathrm{g}^{\left(\mathrm{1}\right)} \left({z}\right)}{\mathrm{g}\left({z}\right)}} \\ $$ Answered by MrGaster last updated on 04/May/25…
Question Number 219806 by SdC355 last updated on 02/May/25 $$\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\left(\frac{\mathrm{cos}\left({x}+{h}\right)}{\mathrm{cos}\left({x}\right)}\right)^{\frac{\mathrm{1}}{{h}}} =?? \\ $$ Answered by fantastic last updated on 02/May/25 $${cos}\left({y}\right)^{\underset{{y}} {\mathrm{1}}} \\ $$…
Question Number 219800 by SdC355 last updated on 02/May/25 $${y}^{\left(\mathrm{2}\right)} \left({t}\right)=\left(\mathrm{1}−{e}^{{t}} \right){y}\left({t}\right)+{y}^{\left(\mathrm{1}\right)} \left({t}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 219801 by SdC355 last updated on 02/May/25 $$\underset{{h}\rightarrow\infty} {\mathrm{lim}}\:{h}^{\nu} {J}_{\nu} \left({h}\right)=?? \\ $$ Answered by MrGaster last updated on 02/May/25 $$\mathrm{lim}_{{h}\rightarrow\infty} \:{h}^{\nu} {J}_{\nu}…
Question Number 219796 by SdC355 last updated on 02/May/25 $$\mathrm{Solve} \\ $$$${y}^{\left(\mathrm{2}\right)} \left({t}\right)=\left({y}\left({t}\right)\right)^{\mathrm{2}} −{ay}^{\left(\mathrm{1}\right)} \left({t}\right)−{by}\left({t}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 219797 by SdC355 last updated on 02/May/25 $$\mathrm{solve} \\ $$$$\left({y}^{\left(\mathrm{2}\right)} \left({t}\right)\right)^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{1}+{y}\left({t}\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 219798 by SdC355 last updated on 02/May/25 $$\mathrm{solve}\: \\ $$$${y}^{\left(\mathrm{2}\right)} \left({t}\right)={y}^{\left(\mathrm{1}\right)} \left({t}\right){e}^{−{y}\left({t}\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com