Question Number 115705 by mnjuly1970 last updated on 27/Sep/20 $$\:\:\:\:\:…\:{nice}\:\:\:{math}\:… \\ $$$$ \\ $$$$\:\:\:\:{find}\::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\Phi=\int_{\mathrm{0}} ^{\:\infty} \left({sin}\left({x}\right)−{cos}\left({x}\right)\:\right){ln}\left({x}\right){dx}=??? \\ $$$$ \\…
Question Number 115516 by bobhans last updated on 26/Sep/20 $${Find}\:{the}\:{supremum}\:{and}\:{the}\:{infimum} \\ $$$${of}\:\frac{{x}}{\mathrm{sin}\:{x}}\:{on}\:{the}\:{interval}\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{2}}\:\right] \\ $$ Commented by john santu last updated on 26/Sep/20 $${infimum}\:{y}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}}{\mathrm{sin}\:{x}}\:=\:\mathrm{1} \\…
Question Number 49935 by ajfour last updated on 12/Dec/18 Commented by ajfour last updated on 12/Dec/18 $${Find}\:{maximum}\:{coloured}\:{area}\:{if} \\ $$$${l}=\:\mathrm{1}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last…
Question Number 49877 by ajfour last updated on 11/Dec/18 Commented by ajfour last updated on 11/Dec/18 $${Find}\:{maximum}\:{area}\:{in}\:{blue}. \\ $$ Answered by mr W last updated…
Question Number 49845 by mhozhez last updated on 11/Dec/18 $${y}^{{xsiny}} +{x}^{{ysinx}} =\mathrm{1} \\ $$$${determine}\:\frac{{dy}}{{dx}} \\ $$ Commented by MJS last updated on 11/Dec/18 $$\mathrm{try}\:\mathrm{this}\:\mathrm{for}\:\mathrm{yourself}.\:\mathrm{the}\:\mathrm{method}\:\mathrm{is}\:\mathrm{simple}: \\…
Question Number 180900 by alcohol last updated on 19/Nov/22 $${show}\:{that}\:\int_{\mathrm{1}} ^{\:+\infty} \left(\frac{{x}−\lfloor{x}\rfloor}{{x}^{\mathrm{2}} }\right){dx}\:=\:\mathrm{1}\:−\:\gamma \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 115302 by mnjuly1970 last updated on 24/Sep/20 $$\:\:\:\:\:\:\:…\:{nice}\:\:{math}… \\ $$$$\:\:\:\:\:{find} \\ $$$$\:\:\:\:{lim}_{{n}\rightarrow\infty\:\:} \left\{\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\int_{{k}−\mathrm{1}} ^{\:\:{k}} {tan}^{−\mathrm{1}} \left(\frac{{nx}−{nk}}{{kx}+{n}^{\mathrm{2}} }\right){dx}\right\} \\ $$$$\: \\ $$…
Question Number 115273 by mnjuly1970 last updated on 24/Sep/20 $$\:\:\:\:\:\:\:\:…\:{advanced}\:\:{mathematics}… \\ $$$$ \\ $$$$\:\:\:\:\:{evaluate}::: \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Delta=\int_{\mathrm{0}} ^{\:\infty} \:\frac{{cos}\left({ln}\left({x}\right)\right)}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }\:{dx}\:=??? \\ $$$$ \\ $$$$\:\:\:\:\:\:\:…{m}.{n}.{july}.\mathrm{1970}……
Question Number 115260 by bobhans last updated on 24/Sep/20 $${Let}\:{f}\:{be}\:{a}\:{real}\:{valued}\:{function}\:{defined} \\ $$$${on}\:{the}\:{interval}\:\left(−\mathrm{1},\mathrm{1}\right)\:{such}\:{that}\: \\ $$$${e}^{−{x}} .{f}\left({x}\right)=\mathrm{2}+\underset{\mathrm{0}} {\overset{{x}} {\int}}\:\sqrt{{t}^{\mathrm{4}} +\mathrm{1}}\:{dt}\:\forall{x}\in\left(−\mathrm{1},\mathrm{1}\right) \\ $$$${and}\:{let}\:{g}\:{be}\:{the}\:{inverse}\:{function}\:{of}\:{f} \\ $$$$.\:{Find}\:{the}\:{value}\:{of}\:{g}'\left(\mathrm{2}\right). \\ $$ Commented…
Question Number 115222 by mnjuly1970 last updated on 24/Sep/20 $$\:\:\:\:\:\:….\:{nice}\:\:{math}\:… \\ $$$$ \\ $$$$\:\:\:\:{nice}\:\:{integral}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}\::: \\ $$$$\Psi=\mathrm{9}\int_{\mathrm{0}} ^{\:\infty} {x}^{\mathrm{5}} {e}^{−{x}^{\mathrm{3}} } {ln}\left(\mathrm{1}+{x}\right){dx}\:\overset{???} {=}\:\Gamma\left(\frac{\mathrm{1}}{\mathrm{3}}\right)−\Gamma\left(\frac{\mathrm{2}}{\mathrm{3}}\right)+\Gamma\left(\frac{\mathrm{3}}{\mathrm{3}}\right)\:\: \\…