Question Number 65464 by aliesam last updated on 30/Jul/19 Commented by mathmax by abdo last updated on 30/Jul/19 $${let}\:\:{A}\left({x}\right)\:={x}\left({x}+\mathrm{1}\right){ln}\left(\frac{{x}+\mathrm{1}}{{x}}\right)−{x}\:\:\:\:{we}\:{have}\:{for}\:{x}\in{V}\left(+\infty\right) \\ $$$${ln}\left(\frac{{x}+\mathrm{1}}{{x}}\right)\:={ln}\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)\:=\frac{\mathrm{1}}{{x}}−\frac{\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} }\:+{o}\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)\: \\ $$$${A}\left({x}\right)\:=\left({x}^{\mathrm{2}}…
Question Number 65463 by aliesam last updated on 30/Jul/19 Answered by MJS last updated on 31/Jul/19 $$\mathrm{i}^{{an}} =\mathrm{cos}\:\frac{{an}\pi}{\mathrm{2}}\:+\mathrm{i}\:\mathrm{sin}\:\frac{{an}\pi}{\mathrm{2}} \\ $$$$\mathrm{imag}\:\left(\mathrm{i}^{{n}} +\mathrm{i}^{\mathrm{2}{n}} +\mathrm{i}^{\mathrm{3}{n}} \right)\:=\mathrm{0} \\ $$$$\mathrm{sin}\:\frac{{n}\pi}{\mathrm{2}}\:+\mathrm{sin}\:{n}\pi\:+\mathrm{sin}\:\frac{\mathrm{3}{n}\pi}{\mathrm{2}}\:=\mathrm{0}…
Question Number 130994 by mnjuly1970 last updated on 31/Jan/21 $$\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:\:{integral}\:… \\ $$$$\:\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \left(\frac{{e}^{−{x}} {sin}\left(\mathrm{2}{x}\right)}{{sinh}\left({x}\right)}\right){dx}=? \\ $$$$ \\ $$ Answered by mindispower last…
Question Number 130992 by benjo_mathlover last updated on 31/Jan/21 $$\mathrm{If}\:\mathrm{I}\:=\:\frac{\mathrm{V}}{\mathrm{R}}\:\mathrm{and}\:\mathrm{V}=\mathrm{250}\:\mathrm{volts}\:\mathrm{and}\:\mathrm{R}=\mathrm{50}\:\mathrm{ohms} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{change}\:\mathrm{in}\:\mathrm{I}\:\mathrm{resulting}\:\mathrm{from}\:\mathrm{an}\: \\ $$$$\mathrm{increase}\:\mathrm{of}\:\mathrm{1}\:\mathrm{volt}\:\mathrm{in}\:\mathrm{V}\:\mathrm{and}\:\mathrm{increase}\:\mathrm{of}\:\mathrm{0}.\mathrm{5}\:\mathrm{ohm} \\ $$$$\mathrm{in}\:\mathrm{R}. \\ $$ Answered by EDWIN88 last updated on 31/Jan/21…
Question Number 65457 by behi83417@gmail.com last updated on 30/Jul/19 $$\begin{cases}{\frac{\boldsymbol{\mathrm{a}}}{\boldsymbol{\mathrm{b}}}+\frac{\boldsymbol{\mathrm{b}}−\boldsymbol{\mathrm{a}}}{\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{a}}}=\mathrm{2}\sqrt{\mathrm{3}}}\\{\frac{\boldsymbol{\mathrm{b}}}{\boldsymbol{\mathrm{a}}}+\frac{\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{a}}}{\boldsymbol{\mathrm{b}}−\boldsymbol{\mathrm{a}}}=\mathrm{3}\sqrt{\mathrm{2}}}\end{cases}\:\:\:\:\:\left[\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\in\boldsymbol{\mathrm{R}},\boldsymbol{\mathrm{a}}\neq\boldsymbol{\mathrm{b}}\right] \\ $$ Answered by mr W last updated on 30/Jul/19 $${let}\:{t}=\frac{{a}}{{b}} \\ $$$${eqn}.\:\mathrm{1}\:\Rightarrow{t}+\frac{\mathrm{1}−{t}}{\mathrm{1}+{t}}=\mathrm{2}\sqrt{\mathrm{3}}\:\:\:\:\:\:…\left({i}\right) \\ $$$${eqn}.\:\mathrm{2}\:\Rightarrow\frac{\mathrm{1}}{{t}}+\frac{\mathrm{1}+{t}}{\mathrm{1}−{t}}=\mathrm{3}\sqrt{\mathrm{2}}\:\:\:\:…\left({ii}\right)…
Question Number 65455 by mathmax by abdo last updated on 30/Jul/19 $${find}\:{U}_{{n}} =\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{x}} }{\mathrm{2}^{{x}^{\mathrm{2}} } \left({x}^{\mathrm{2}} \:+\mathrm{4}{n}^{\mathrm{2}} \right)}{dx}\:\:\:\:\:\left({n}\:{from}\:{N}\:{and}\:{n}\geqslant\mathrm{1}\right) \\ $$$${study}\:{nature}\:{of}\:{the}\:{serie}\:\:\Sigma\:\mathrm{2}^{{n}^{\mathrm{2}} } {U}_{{n}} \\…
Question Number 65450 by imron876 last updated on 30/Jul/19 Commented by Prithwish sen last updated on 30/Jul/19 $$\left.\mathrm{1}\right)\:\mathrm{a}=\mathrm{b}=\mathrm{c}=\mathrm{d}=\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\mathrm{a}=\mathrm{c}=\mathrm{1},\mathrm{b}=\mathrm{d}=\mathrm{0} \\ $$$$\left.\mathrm{3}\right)\mathrm{b}=\mathrm{d}=\mathrm{1},\mathrm{a}=\mathrm{c}=\mathrm{0} \\ $$$$\left.\mathrm{4}\right)\mathrm{a}=\mathrm{1}\:\mathrm{c}=−\mathrm{1}\:\mathrm{b}=\mathrm{d}=\mathrm{0} \\…
Question Number 65446 by LPM last updated on 30/Jul/19 $$\:\:\:\:\mathrm{10}^{\mathrm{x}} \:=\:\mathrm{x}^{\mathrm{1000}} \:\Rightarrow\:\mathrm{x}=? \\ $$ Commented by MJS last updated on 30/Jul/19 $${a}^{{x}} ={x}^{{b}} \\ $$$${x}\mathrm{ln}\:{a}\:={b}\mathrm{ln}\:{x}…
Question Number 65445 by mathmax by abdo last updated on 30/Jul/19 $${find}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left({cost}\:+{xsint}\right){dt}\:\:\: \\ $$ Commented by Prithwish sen last updated on 30/Jul/19 $$\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\pi−\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{8}}\:\mathrm{ln}\mid\mathrm{1}+\mathrm{x}^{\mathrm{2}}…
Question Number 130978 by I want to learn more last updated on 31/Jan/21 Commented by I want to learn more last updated on 31/Jan/21 $$\mathrm{The}\:\mathrm{question}\:\mathrm{start}\:\mathrm{this}\:\mathrm{way}:…