Question Number 143048 by 0731619 last updated on 09/Jun/21 Answered by mindispower last updated on 09/Jun/21 $$=\underset{{n}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\sqrt{\Gamma\left({n}\right)}−\mathrm{1}/\left(\Gamma\left({n}\right)−\mathrm{1}\right)=\frac{\mathrm{1}}{\:\sqrt{\Gamma\left({n}\right)}+\mathrm{1}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Terms of Service…
Question Number 143051 by mnjuly1970 last updated on 09/Jun/21 $$\:\:\:\:\:\:\:_{\ast\ast\ast\ast\ast} ::\:\:{Lobachevsky}\:{Integral}\:::_{\ast\ast\ast\ast\ast} \\ $$$$\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}:=\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{s}{in}^{\mathrm{2}} \left(\:{tan}\left({x}\right)\right)}{{x}^{\:\mathrm{2}} }{dx}\overset{?} {=}\frac{\pi}{\mathrm{2}} \\ $$$$\:\:\:\:………. \\ $$ Answered by Olaf_Thorendsen…
Question Number 77513 by BK last updated on 07/Jan/20 Commented by Kunal12588 last updated on 07/Jan/20 -99631646050232081463391082912554874214147786127212261300098296284926069581800964669753771227589064527729684298473399551387739150433334227370085293404740389579109830756667470298828368996394719909762120 Commented by MJS last updated on 07/Jan/20 $$\mathrm{let}'\mathrm{s}\:\mathrm{just}\:\mathrm{give}\:\mathrm{it}\:\mathrm{a}\:\mathrm{name}…
Question Number 143045 by 0731619 last updated on 09/Jun/21 Answered by Dwaipayan Shikari last updated on 09/Jun/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}−{x}^{{n}} }{\mathrm{1}−{x}}{dx}=−\gamma+\psi\left({n}+\mathrm{1}\right) \\ $$$$\underset{{n}\rightarrow\mathrm{3}} {\mathrm{lim}}\frac{−\gamma−\mathrm{1}.\mathrm{833}+\psi\left({n}+\mathrm{1}\right)}{\Gamma\left({n}+\mathrm{1}\right)−\mathrm{6}}\overset{{Lhopital}} {=}\frac{\psi'\left({n}+\mathrm{1}\right)}{\Gamma'\left({n}+\mathrm{1}\right)}=\frac{\psi'\left(\mathrm{4}\right)}{\psi\left(\mathrm{4}\right)\Gamma\left(\mathrm{4}\right)}…
Question Number 143047 by 0731619 last updated on 09/Jun/21 Answered by JDamian last updated on 09/Jun/21 $$\Sigma\frac{\mathrm{1}}{{k}^{\mathrm{3}} }\:\:\mathrm{is}\:\mathrm{unknown} \\ $$ Commented by ArielVyny last updated…
Question Number 143046 by 0731619 last updated on 09/Jun/21 Answered by mindispower last updated on 09/Jun/21 $${x}^{{x}^{{x}} } ={f}\left({x}\right)\Rightarrow{ln}\left({fx}\right)={f}\left({x}\right){ln}\left({x}\right) \\ $$$${ln}\left({f}\left({x}\right)\right){e}^{−{ln}\left({f}\left({x}\right)\right)} ={ln}\left({x}\right) \\ $$$$\Rightarrow−{ln}\left({f}\left({x}\right)\right)={W}\left(−{ln}\left({x}\right)\right) \\…
Question Number 143041 by bramlexs22 last updated on 09/Jun/21 $${If}\:{f}\left({x}\right)={x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{2}\:{then}\:{the}\:{value} \\ $$$${of}\:\left(\mathrm{1}−\frac{\mathrm{2}}{{f}\left(\mathrm{1}\right)}\right)\left(\mathrm{1}−\frac{\mathrm{2}}{{f}\left(\mathrm{2}\right)}\right)\left(\mathrm{1}−\frac{\mathrm{2}}{{f}\left(\mathrm{3}\right)}\right)…\left(\mathrm{1}−\frac{\mathrm{2}}{{f}\left(\mathrm{2021}\right)}\right)=? \\ $$ Commented by SLVR last updated on 13/Jun/21 $${whats}\:{the}\:{answwer}???{and}\:{solution} \\ $$…
Question Number 77506 by BK last updated on 07/Jan/20 Commented by BK last updated on 07/Jan/20 $$\left.\mathrm{A}\left.\right)\left.\mathrm{2}\left.\mathrm{011}\:\:\:\:\:\:\:\:\:\:\:\mathrm{B}\right)\mathrm{2012}\:\:\:\:\:\:\:\:\:\:\:\mathrm{C}\right)\mathrm{4021}\:\:\:\:\:\:\:\:\:\mathrm{D}\right)\mathrm{4023} \\ $$ Commented by MJS last updated on…
Question Number 143043 by 0731619 last updated on 09/Jun/21 Answered by Dwaipayan Shikari last updated on 09/Jun/21 $${y}={x}!^{{x}!} \\ $$$${log}\left({y}\right)={x}!{log}\left({x}!\right) \\ $$$${log}\left({y}\right)=\Gamma\left({x}+\mathrm{1}\right){log}\left(\Gamma\left({x}+\mathrm{1}\right)\right) \\ $$$$\frac{{y}'}{{y}}=\Gamma'\left({x}+\mathrm{1}\right){log}\left(\Gamma\left({x}+\mathrm{1}\right)\right)+\Gamma'\left({x}+\mathrm{1}\right) \\…
Question Number 77504 by Maclaurin Stickker last updated on 07/Jan/20 Answered by mr W last updated on 07/Jan/20 $${say}\:{the}\:{radius}\:{of}\:{large}\:{outer}\:{circle}={R} \\ $$ Commented by mr W…