Question Number 9113 by hmhjkk last updated on 19/Nov/16 $$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{x}^{\mathrm{2}} /\mathrm{x}^{\mathrm{2}} +\mathrm{1}=\mathrm{0} \\ $$ Commented by sou1618 last updated on 19/Nov/16 $$\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 9109 by tawakalitu last updated on 18/Nov/16 $$\mathrm{if}\:\:\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{log}_{\mathrm{a}} \mathrm{xy}} \\ $$$$\mathrm{find}\:\:\frac{\mathrm{dy}}{\mathrm{dx}} \\ $$ Answered by mrW last updated on 19/Nov/16 $${y}={x}^{{log}_{{a}} {xy}} \\…
Question Number 9086 by tawakalitu last updated on 17/Nov/16 $$\mathrm{Prove}\:\mathrm{the}\:\mathrm{limit}.,\:\:\:\frac{\mathrm{sin}\left(\theta/\mathrm{2}\right)}{\left(\theta/\mathrm{2}\right)}\:=\:\mathrm{1} \\ $$ Commented by 123456 last updated on 17/Nov/16 $$\underset{\theta\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\theta/\mathrm{2}}{\theta/\mathrm{2}}=\underset{\alpha\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\alpha}{\alpha} \\ $$$$\alpha=\theta/\mathrm{2} \\…
Question Number 74601 by ~blr237~ last updated on 27/Nov/19 $${solve}\:\:\:{y}''+\:{a}\left({x}\right){y}={b}\left({x}\right)\: \\ $$$${the}\:\:{general}\:\:{form}\:{of}\:\:{the}\:{solution}\:{if}\:\:{possible} \\ $$$${or}\:\:{juzt}\:{a}\:{solving}\:{metbod} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 74542 by Cmr 237 last updated on 25/Nov/19 $$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\int\left(\boldsymbol{{ln}}\left(\boldsymbol{{x}}\right)\boldsymbol{{e}}^{\boldsymbol{{x}}} \right)\boldsymbol{{dx}}=??? \\ $$ Answered by MJS last updated…
Question Number 74536 by mhmd last updated on 25/Nov/19 $${find}\:{limz}\Rightarrow\mathrm{0}\:\:\left({xy}^{\mathrm{2}} /{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)\:{pleas}\:{sir}\:{help}\:{me}\: \\ $$ Answered by mind is power last updated on 26/Nov/19 $$\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)}…
Question Number 8996 by Basant007 last updated on 11/Nov/16 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{derivative}\:\mathrm{of}\:\mathrm{sin}\:^{\mathrm{2}} \mathrm{2x} \\ $$ Commented by FilupSmith last updated on 13/Nov/16 $${y}=\mathrm{sin}^{\mathrm{2}} \left(\mathrm{2}{x}\right) \\ $$$${u}=\mathrm{sin}\left(\mathrm{2}{x}\right)\:\Rightarrow\:{du}=\mathrm{2cos}\left(\mathrm{2}{x}\right){dx} \\…
Question Number 140055 by mnjuly1970 last updated on 03/May/21 $$\:\:\:\:\:\: \\ $$$$\:\:{prove}\:\:{that}\:: \\ $$$$\:\:\:\:\:\:\:\:\Omega:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{1}−{e}^{−{x}} }{\mathrm{1}+{e}^{\mathrm{2}{x}} }\:.\frac{{dx}}{{x}}\:={ln}\left(\frac{\Gamma^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)}{\mathrm{4}\sqrt{\mathrm{2}\pi}}\:\right) \\ $$$$\:\Theta:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\frac{\mathrm{2}{n}+\mathrm{1}}{\mathrm{2}{n}}\right)^{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} } \overset{??}…
Question Number 140050 by mnjuly1970 last updated on 03/May/21 $$\:\:\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\:\:\:\phi\::={lim}_{{n}\rightarrow\infty} \frac{{n}}{\:\sqrt{\mathrm{2}{k}}}\:.\sqrt{\mathrm{1}−{cos}^{{k}} \left(\frac{\mathrm{2}\pi}{{n}}\right)}\:=\pi \\ $$$$\:\:\:\:\:\:\:\:……………. \\ $$$$ \\ $$ Answered by Kamel last updated…
Question Number 139949 by mnjuly1970 last updated on 02/May/21 $$\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:………{nice}\:….\:\ast\:….\ast\:….\:\ast\:….{calculus}\left({I}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\:\:{lim}_{{x}\rightarrow\mathrm{0}^{+} } \left(\sqrt[{\mathrm{3}}]{{cos}\left(\sqrt{{x}}\:\right.}\:\right)^{{cot}\left({x}\right)} =?? \\ $$$$\:\:\:\:\:\:\:\:{solution}……… \\ $$$$\:\:\:\:\:\:\:{sin}\left({x}\right)\:\approx\:{x}\:\:\:\:\:\:\:\:\left({x}\:\rightarrow\:\mathrm{0}\:\right) \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\phi}:=\:\:{lim}_{{x}\rightarrow\mathrm{0}^{+} } \left\{\left({cos}\left(\sqrt{{x}}\:\right)\right)^{\frac{\mathrm{1}}{\mathrm{3}}}…