Question Number 155136 by amin96 last updated on 25/Sep/21 $$\boldsymbol{{prove}}\:\boldsymbol{{that}} \\ $$$$\frac{\boldsymbol{\mathrm{log}}^{\mathrm{2}} \left(\mathrm{2}\right)}{\mathrm{2}}\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\boldsymbol{\varphi}\left(\boldsymbol{{n}}\right)}{\left(\boldsymbol{{n}}+\mathrm{1}\right)^{\mathrm{2}} \mathrm{2}^{\boldsymbol{{n}}} }+\boldsymbol{\mathrm{log}}\left(\mathrm{2}\right)\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\boldsymbol{\varphi}\left({n}\right)}{\left(\boldsymbol{{n}}+\mathrm{1}\right)^{\mathrm{3}} \mathrm{2}^{\boldsymbol{{n}}} }+\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\boldsymbol{\varphi}\left({n}\right)}{\left(\boldsymbol{{n}}+\mathrm{1}\right)^{\mathrm{4}} \mathrm{2}^{\boldsymbol{{n}}} }=…
Question Number 89600 by jagoll last updated on 18/Apr/20 $$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{y}+\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} }}{\mathrm{x}}\: \\ $$ Commented by mr W last updated on 18/Apr/20 $$\frac{{dy}}{{dx}}=\frac{{y}}{{x}}+\sqrt{\mathrm{1}−\left(\frac{{y}}{{x}}\right)^{\mathrm{2}} } \\…
Question Number 155133 by amin96 last updated on 25/Sep/21 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{3}} }=? \\ $$ Answered by mnjuly1970 last updated on 26/Sep/21 $$\:\:\:\frac{\pi^{\:\mathrm{3}} }{\mathrm{32}}…
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Question Number 89599 by 20000193 last updated on 18/Apr/20 Commented by john santu last updated on 18/Apr/20 $$\left.\mathrm{4}{a}\right)\:\mathrm{tan}\:\left({A}+{C}\right)\:=\frac{\mathrm{tan}\:{A}+\mathrm{tan}\:{C}}{\mathrm{1}−\mathrm{tan}\:{A}.\mathrm{tan}\:{C}} \\ $$$$\:{case}\:\left(\mathrm{1}\right)\:=\:\frac{\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\:+\:\sqrt{\mathrm{3}}}{\mathrm{1}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}.\sqrt{\mathrm{3}}}\:=\:\infty\:\left({undefined}\:\right) \\ $$$${case}\:\left(\mathrm{2}\right)\:=\:\frac{\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\:−\:\sqrt{\mathrm{3}}}{\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}.\sqrt{\mathrm{3}}}\:=\:\frac{−\mathrm{2}}{\mathrm{2}\sqrt{\mathrm{3}}}\:=\:−\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}} \\ $$$${case}\:\left(\mathrm{3}\right)\:=\:\frac{\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}+\sqrt{\mathrm{3}}}{\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}.\sqrt{\mathrm{3}}}\:=\:\frac{\mathrm{4}}{\mathrm{2}\sqrt{\mathrm{3}}}\:=\:\frac{\mathrm{2}}{\:\sqrt{\mathrm{3}}} \\…
Question Number 155135 by amin96 last updated on 25/Sep/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \left(\frac{\boldsymbol{\mathrm{log}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}\right)−\boldsymbol{\mathrm{log}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{y}}}\right)}{\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{log}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}\right)\right)−\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{log}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{y}}}\right)\right)}\right)^{\mathrm{2}} \boldsymbol{\mathrm{dxdy}}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 89596 by A8;15: last updated on 18/Apr/20 Commented by john santu last updated on 18/Apr/20 $$\sqrt{\frac{{x}}{\mathrm{1}−{x}}}\:=\:{t}\:\Rightarrow\:{x}\:=\:\frac{{t}^{\mathrm{2}} }{{t}^{\mathrm{2}} +\mathrm{1}} \\ $$$$\left.{dx}\:=\:\frac{\mathrm{2}{t}}{\left({t}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }\:{dt}\:\right]\: \\…
Question Number 155134 by amin96 last updated on 25/Sep/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \boldsymbol{\mathrm{sin}}^{\mathrm{2}\boldsymbol{\mathrm{n}}} \left({x}\right){dx}=? \\ $$ Answered by phanphuoc last updated on 26/Sep/21 $$\pi/\mathrm{24}^{{n}} .\begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}\:\:\:\:\:\:{this}\:{is}\:{wallis}'={intergral} \\…
Question Number 89592 by M±th+et£s last updated on 18/Apr/20 $${cos}\left({x}\right)={k}\: \\ $$$$\left\{−\mathrm{1}\leqslant{k}<\mathrm{0}\right\} \\ $$ Commented by mr W last updated on 18/Apr/20 $${i}\:{don}'{t}\:{understand}\:{what}'{s}\:{your}\:{problem}. \\ $$$$…
Question Number 24057 by NECx last updated on 12/Nov/17 $${A}\:{block}\:{of}\:{ice}\:{slides}\:{down}\:{a}\:\mathrm{45}° \\ $$$${incline}\:{plane}\:{in}\:{twice}\:{the}\:{time}\:{it} \\ $$$${takes}\:{to}\:{slide}\:{down}\:{a}\:\mathrm{45}°\:{frictionless} \\ $$$${incline}\:{plane}.{What}\:{is}\:{the}\:{coefficient} \\ $$$${of}\:{kinetic}\:{friction}\:{between}\:{the} \\ $$$${ice}\:{block}\:{and}\:{the}\:{incline}\:{plqne}. \\ $$ Answered by mrW1…