Question Number 210112 by klipto last updated on 31/Jul/24 $$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{n}}} }{\left(\boldsymbol{\mathrm{x}}+\mathrm{1}\right)\left(\boldsymbol{\mathrm{ax}}+\boldsymbol{\mathrm{b}}\right)}\boldsymbol{\mathrm{dx}}=\frac{\left(\frac{\boldsymbol{\mathrm{b}}}{\boldsymbol{\mathrm{a}}}\right)^{\boldsymbol{\mathrm{n}}} −\mathrm{1}}{\boldsymbol{\mathrm{b}}−\boldsymbol{\mathrm{a}}}\boldsymbol{\pi\mathrm{csc}}\left(\boldsymbol{\pi\mathrm{n}}\right)\:\boldsymbol{\mathrm{a}}>\mathrm{0},\boldsymbol{\mathrm{b}}>\mathrm{0},\mid\boldsymbol{\mathrm{n}}\mid<\mathrm{1} \\ $$$$\boldsymbol{\mathrm{guys}}\:\boldsymbol{\mathrm{kill}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{let}}\:\boldsymbol{\mathrm{me}}\:\boldsymbol{\mathrm{see}} \\ $$ Answered by Spillover last updated…
Question Number 210044 by maths_plus last updated on 29/Jul/24 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }\right)…\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)=??? \\ $$ Commented by Frix last updated on 29/Jul/24 $$\underset{{k}=\mathrm{2}} {\overset{{n}}…
Question Number 210078 by Spillover last updated on 29/Jul/24 $${Find}\:{the}\:{directional}\:{derivative}\:{of} \\ $$$${f}\left({x},{y}\right)=\mathrm{4}{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} {y}^{\mathrm{2}} \:\:\:{in}\:{the}\:{direction}\:{given} \\ $$$${by}\:{the}\:{angle}\:\theta=\frac{\pi}{\mathrm{3}}\: \\ $$$${and}\:{also}\:{Evaluate}\:{directional}\:{derivatives} \\ $$$${at}\:{the}\:{point}\:\left(\mathrm{1},\mathrm{2}\right) \\ $$ Answered by…
Question Number 210079 by Spillover last updated on 30/Jul/24 $${Find}\:{directional}\:{derivatives}\left({D}_{{v}} \right){of}\:\: \\ $$$${f}\left({x},{y},{z}\right)=\mathrm{3}{xy}^{\mathrm{3}} −\mathrm{2}{xz}^{\mathrm{2}} \:\:{in}\:{the}\:{direction}\:{of}\:{the} \\ $$$${v}=\mathrm{2}{i}−\mathrm{3}{j}+\mathrm{6}{k}. \\ $$$${then}\:{Evaluate}\:{directional}\:{derivatives}\: \\ $$$${at}\:{the}\:{point}\:\left(\mathrm{3},\mathrm{1},−\mathrm{2}\right) \\ $$ Terms of…
Question Number 210072 by peter frank last updated on 29/Jul/24 Answered by Frix last updated on 29/Jul/24 $$\mathrm{The}\:\mathrm{incircle}\:\mathrm{of}\:\mathrm{a}\:\mathrm{rectangular}\:\mathrm{triangle}\:\mathrm{with} \\ $$$$\mathrm{sides}\:{a},\:{b},\:\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }\:\mathrm{is}\:\frac{{a}+{b}−\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }}{\mathrm{2}}\:\:\:\:\:\left(\ast\right) \\…
Question Number 210036 by peter frank last updated on 29/Jul/24 Answered by Prithwish last updated on 29/Jul/24 $${ab}=\left(\frac{\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} \theta}{\mathrm{cos}\:\theta}\right)\left(\frac{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} \theta}{\mathrm{sin}\:\theta}\right) \\ $$$${ab}=\mathrm{sin}\:\theta\mathrm{cos}\:\theta \\ $$$${a}^{\mathrm{2}} +\overset{\mathrm{2}}…
Question Number 210032 by klipto last updated on 29/Jul/24 $$\int_{\mathrm{6}} ^{\mathrm{0}} \left(\mathrm{2}+\mathrm{5}\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{e}}^{\frac{\mathrm{1}}{\mathrm{3}}\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{dx}} \\ $$ Answered by Sutrisno last updated on 29/Jul/24 $$=\int_{\mathrm{6}} ^{\mathrm{0}} \mathrm{2}{e}^{\frac{\mathrm{1}}{\mathrm{3}}{x}}…
Question Number 210034 by peter frank last updated on 29/Jul/24 Commented by peter frank last updated on 29/Jul/24 $$\mathrm{solve}\:\mathrm{for}\:\mathrm{x} \\ $$ Commented by Frix last…
Question Number 210060 by SANOGO last updated on 29/Jul/24 $$\int_{\mathrm{0}} ^{+\infty} \frac{{n}}{{sin}^{\mathrm{2}} {n}+{nx}^{\mathrm{2}} }{dx} \\ $$$$ \\ $$ Answered by mr W last updated on…
Question Number 210031 by MrGHK last updated on 29/Jul/24 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}−\boldsymbol{\mathrm{xcot}}\left(\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\boldsymbol{\mathrm{dx}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com