Question Number 128069 by 0731619177 last updated on 04/Jan/21 Answered by Dwaipayan Shikari last updated on 04/Jan/21 $$\frac{{d}}{{dx}}\left({x}!\right)=\Gamma'\left({x}+\mathrm{1}\right)=\Gamma\left({x}+\mathrm{1}\right)\psi\left({x}+\mathrm{1}\right)={x}!\left(−\gamma+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}}−\frac{\mathrm{1}}{{n}+{x}}\right) \\ $$ Answered by A8;15:…
Question Number 128065 by 0731619177 last updated on 04/Jan/21 Commented by mnjuly1970 last updated on 04/Jan/21 $${lim}_{{n}\rightarrow\infty\:\:\:} \underset{{k}=\mathrm{1}\:} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{k}^{\mathrm{2}} }=\frac{\pi^{\mathrm{2}} }{\mathrm{6}} \\ $$$${lim}_{{n}\rightarrow\infty} \left(\underset{{k}=\mathrm{1}}…
Question Number 62523 by Tawa1 last updated on 22/Jun/19 Answered by $@ty@m last updated on 22/Jun/19 $${x}=\mathrm{90}−\left(\mathrm{90}−\mathrm{34}\right)=\mathrm{34} \\ $$$${y}={x}+\mathrm{90}=\mathrm{34}+\mathrm{90}=\mathrm{124} \\ $$ Terms of Service Privacy…
Question Number 128057 by bramlexs22 last updated on 04/Jan/21 $$\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{1}}{\mathrm{1}−\mathrm{xy}^{\mathrm{2}} }\:\mathrm{dx}\:\mathrm{dy}\:=? \\ $$ Answered by liberty last updated on 04/Jan/21 $$\:\frac{\mathrm{1}}{\mathrm{1}−\mathrm{xy}^{\mathrm{2}}…
Question Number 62519 by azizullah last updated on 22/Jun/19 Answered by $@ty@m last updated on 22/Jun/19 $$\left({i}\right)\:{A}={bh}−\frac{\mathrm{1}}{\mathrm{2}}{bh}=\frac{\mathrm{1}}{\mathrm{2}}{bh} \\ $$$$\Rightarrow\mathrm{2}{A}={bh} \\ $$$$\left({ii}\right)\:{A}={ab}−\mathrm{4}{x}^{\mathrm{2}} \\ $$ Commented by…
Question Number 128052 by bramlexs22 last updated on 04/Jan/21 $$\:\mathrm{I}\:=\:\int\:\mathrm{arctan}\:\left(\frac{\mathrm{x}−\mathrm{2}}{\mathrm{x}+\mathrm{2}}\right)\:\mathrm{dx}\: \\ $$ Answered by liberty last updated on 04/Jan/21 $$\mathrm{I}\:=\:\mathrm{x}\:\mathrm{arctan}\:\left(\frac{\mathrm{x}−\mathrm{2}}{\mathrm{x}+\mathrm{2}}\right)−\int\:\mathrm{x}\left(\frac{\mathrm{1}}{\mathrm{1}+\left(\frac{\mathrm{x}−\mathrm{2}}{\mathrm{x}+\mathrm{2}}\right)^{\mathrm{2}} }.\:\frac{\mathrm{4}}{\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{2}} }\right)\mathrm{dx} \\ $$$$\mathrm{I}=\mathrm{x}\:\mathrm{arctan}\:\left(\frac{\mathrm{x}−\mathrm{2}}{\mathrm{x}+\mathrm{2}}\right)−\int\:\frac{\mathrm{2x}}{\mathrm{x}^{\mathrm{2}} +\mathrm{4}}\:\mathrm{dx}…
Question Number 62517 by Tawa1 last updated on 22/Jun/19 Commented by $@ty@m last updated on 22/Jun/19 $${what}\:{is}\:{meant}\:{by}\:{BC}=\begin{pmatrix}{\mathrm{3}}\\{\mathrm{1}}\end{pmatrix}\: \\ $$$${pl}.\:{clarify}\:{this}\:{notation}. \\ $$ Commented by Prithwish sen…
Question Number 128048 by bramlexs22 last updated on 04/Jan/21 $$\:\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{8n}+\mathrm{3}}\:=? \\ $$ Answered by Olaf last updated on 04/Jan/21 $$\mathrm{L}\left(\lambda,\alpha,{s}\right)\:=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{e}^{\mathrm{2}{i}\pi\lambda{n}}…
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Question Number 128038 by Walt123 last updated on 03/Jan/21 $$ \\ $$Resolva a equação abaixo: $$ \\ $$$$\mathrm{5}^{\mathrm{x}} .\mathrm{16}^{\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}}} =\mathrm{100} \\ $$ Answered by MJS_new…