Question Number 131584 by mr W last updated on 06/Feb/21 Commented by mr W last updated on 06/Feb/21 $${find}\:{R}=? \\ $$ Answered by ajfour last…
Question Number 514 by 112358 last updated on 25/Jan/15 $${Determine}\:{the}\:{smallest}\:{value}\:{of} \\ $$$${the}\:{form} \\ $$$${f}\left({u},{v}\right)=\frac{\mathrm{5}{v}^{\mathrm{2}} +\mathrm{5}{u}^{\mathrm{2}} +\mathrm{1}}{\mathrm{2}{u}+{v}} \\ $$$${where}\:{u},{v}\in{R}^{+} . \\ $$ Answered by prakash jain…
Question Number 66048 by aliesam last updated on 08/Aug/19 $$\int\frac{{x}}{\:\sqrt{{ln}\left(\mathrm{1}/{x}\right)}}\:{dx} \\ $$ Commented by Prithwish sen last updated on 08/Aug/19 $$\int\frac{\mathrm{x}}{\:\sqrt{−\mathrm{lnx}}}\mathrm{dx}\:\:\:\mathrm{put}−\mathrm{lnx}\:=\:\mathrm{u}^{\mathrm{2}} \:\Rightarrow\mathrm{dx}=−\mathrm{2ue}^{−\mathrm{u}^{\mathrm{2}} } \\ $$$$=\:−\mathrm{2}\int\mathrm{e}^{−\mathrm{2u}^{\mathrm{2}}…
Question Number 513 by 112358 last updated on 25/Jan/15 $${What}\:{is}\:{the}\:{greatest}\:{common} \\ $$$${divisor}\:{of}\:{the}\:\mathrm{2010}\:{digit}\:{and}\:\mathrm{2005}\:{digit} \\ $$$${numbers}\:{below}? \\ $$$$\mathrm{222}…\mathrm{222}\:\left(\mathrm{2010}\:{of}\:{twos}\right) \\ $$$$\mathrm{777}…\mathrm{777}\:\left(\mathrm{2005}\:{of}\:{sevens}\right) \\ $$ Answered by prakash jain last…
Question Number 131581 by mnjuly1970 last updated on 06/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:\:\:\:{calculus}… \\ $$$$\:\:\:{evaluate}\::: \\ $$$$\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({x}\right)}{{x}}{ln}\left(\frac{{a}+{cos}^{\mathrm{2}} \left({x}\right)}{{b}+{cos}^{\mathrm{2}} \left({x}\right)}\right){dx}=? \\ $$$$ \\ $$ Commented…
Question Number 66046 by olalekan2 last updated on 08/Aug/19 $${find}\:\frac{{dy}}{{dx}}\:{if}\:{y}={x}^{{x}^{{x}} } \\ $$$${help}\:{pls} \\ $$ Commented by Prithwish sen last updated on 08/Aug/19 $$\mathrm{y}=\mathrm{x}^{\mathrm{x}^{\mathrm{x}} }…
Question Number 131580 by Dwaipayan Shikari last updated on 06/Feb/21 $$\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{or}}\:\boldsymbol{\mathrm{disprove}} \\ $$$$\underset{\boldsymbol{{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\boldsymbol{{n}}^{\mathrm{2}} +\mathrm{97}\right)^{\mathrm{2}} }=\frac{\boldsymbol{\pi}^{\mathrm{2}} }{\mathrm{97}\left(\boldsymbol{{e}}^{\boldsymbol{\pi}\sqrt{\mathrm{97}}} −{e}^{−\boldsymbol{\pi}\sqrt{\mathrm{97}}} \right)^{\mathrm{2}} }+\frac{\boldsymbol{\pi}}{\mathrm{388}}.\frac{{e}^{\mathrm{2}\boldsymbol{\pi}\sqrt{\mathrm{97}}} +\mathrm{1}}{\boldsymbol{{e}}^{\mathrm{2}\boldsymbol{\pi}\sqrt{\mathrm{97}}} −\mathrm{1}}+\frac{\mathrm{37635}}{\mathrm{37636}}−\frac{\mathrm{1}}{\:\mathrm{388}\sqrt{\mathrm{97}}} \\ $$…
Question Number 510 by 123456 last updated on 21/Jan/15 $${proof}\:{or}\:{given}\:{a}\:{counter}\:{example}: \\ $$$${if}\:{p},{q}\:{are}\:{prines}\:{with}\:{p}>{q},\:{and}\:\exists{s}\:{prime} \\ $$$${such}\:{s}\in\left({q},{p}\right)\:{then} \\ $$$${p}−{q}\leqslant\underset{{r}\in\left({q},{p}\right),{r}\:{is}\:{prime}} {\sum}{r} \\ $$$$ \\ $$ Commented by prakash jain…
Question Number 66044 by rajesh4661kumar@gmail.com last updated on 08/Aug/19 Answered by Tanmay chaudhury last updated on 08/Aug/19 $$\int\frac{{dx}}{{x}^{\mathrm{5}} \left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{4}} }\right)^{\frac{\mathrm{3}}{\mathrm{4}}} } \\ $$$${t}=\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{4}} }\rightarrow{dt}=\frac{−\mathrm{4}}{{x}^{\mathrm{5}} }{dx}…
Question Number 509 by kth last updated on 25/Jan/15 $$\int{f}\left({x}\right){dx} \\ $$ Answered by 123456 last updated on 21/Jan/15 $${F}\left({x}\right)+{C} \\ $$ Terms of Service…