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Question Number 76250 by Mikael_786 last updated on 25/Dec/19 Commented by Mikael_786 last updated on 25/Dec/19 $${how}\:{to}\:{find}\:{tranform}\:{laplace}\:{invers}? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 10711 by Saham last updated on 23/Feb/17 $$\mathrm{If}\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{x}^{\mathrm{x}} } \:,\:\:\mathrm{find}\:\frac{\mathrm{dy}}{\mathrm{dx}} \\ $$ Answered by mrW1 last updated on 23/Feb/17 $${u}={x}^{{x}} \\ $$$$\mathrm{ln}\:{u}={x}\mathrm{ln}\:{x} \\…
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Question Number 141716 by qaz last updated on 22/May/21 $$\left({x}^{\mathrm{2}} {lnx}\right){y}''−{xy}'+{y}=\mathrm{0} \\ $$ Answered by mnjuly1970 last updated on 23/May/21 $$\:\:{y}_{{p}_{\mathrm{1}} } ={ln}\left({x}\right)+\mathrm{1}\:\:\:\:\:\:\:\:{or}\:\:\:\:{y}_{{p}_{\mathrm{1}} } ={x}…
Question Number 141668 by mnjuly1970 last updated on 22/May/21 $$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:…….{Advanced}\:…\bigstar\:…\bigstar\:…\:{Calculus}……. \\ $$$$\:\:\:\:\:\:\:\:\:{if}\:\:\:\:\Omega\:=\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} \zeta\left({n}\right)}{\mathrm{2}^{{n}} }\:{then}\:{prove} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{that}\:::\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\:=\:{e}^{\Omega−\mathrm{1}} \:\: \\ $$$$\:\:\:\:{proof}\::: \\ $$$$\:\:\:\:{method}\:\left(\mathrm{1}\right):…
Question Number 141512 by mnjuly1970 last updated on 19/May/21 $$ \\ $$$$\:\:\:\underset{{n}=\mathrm{1}\:} {\overset{\infty} {\sum}}\frac{{sin}\left(\frac{\left(\mathrm{2}{n}−\mathrm{1}\right)\pi}{\mathrm{6}}\right)}{\left(\mathrm{2}{n}−\mathrm{1}\right)^{\mathrm{2}} }\:=\:{a}.{G} \\ $$$$\:\:{a}\:=\:?\:\:\:\:\:\:\left({G}:=\:{catalan}\:{constant}\right) \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 141475 by bramlexs22 last updated on 19/May/21 $$\:{Find}\:{the}\:{smallest}\:{value}\:{of}\: \\ $$$$\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:{among}\:{all}\:{values}\:{of} \\ $$$$\:{x}\:\&\:{y}\:{satisfying}\:\mathrm{3}{x}−{y}\:=\:\mathrm{20}\: \\ $$ Answered by MJS_new last updated on 19/May/21…
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Question Number 141378 by mnjuly1970 last updated on 18/May/21 $$\:\:\:{prove}\:{that}:: \\ $$$$\:\:\:\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\prod}}\frac{\left(\mathrm{5}{n}+\mathrm{2}\right)\left(\mathrm{5}{n}+\mathrm{3}\right)}{\left(\mathrm{5}{n}+\mathrm{1}\right)\left(\mathrm{5}{n}+\mathrm{4}\right)}\:=\varphi\: \\ $$$$\:\:\:\:\:\:\:\varphi:=\:\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$ Answered by Dwaipayan Shikari last updated on…