Question Number 115750 by shahria14 last updated on 28/Sep/20 Answered by Dwaipayan Shikari last updated on 28/Sep/20 $$\underset{{x}\rightarrow−\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{log}\left(\mathrm{1}+\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \right)}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }=\mathrm{1} \\ $$$$\mathrm{log}\left(\mathrm{1}+\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \right)=\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{approx}\right)…
Question Number 115733 by bemath last updated on 28/Sep/20 $${Given}\:{xy}\:=\frac{\mathrm{1}}{\mathrm{3}}\:{for}\:{x},{y}\in\mathbb{R}\: \\ $$$${find}\:{min}\:{value}\:{of}\:\frac{\mathrm{4}}{{x}^{\mathrm{6}} }+\frac{\mathrm{9}}{{y}^{\mathrm{6}} } \\ $$ Answered by MJS_new last updated on 28/Sep/20 $${y}=\frac{\mathrm{1}}{\mathrm{3}{x}}\:\Rightarrow\:\frac{\mathrm{4}}{{x}^{\mathrm{6}} }+\frac{\mathrm{9}}{{y}^{\mathrm{6}}…
Question Number 115705 by mnjuly1970 last updated on 27/Sep/20 $$\:\:\:\:\:…\:{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}……