Question Number 131729 by ajfour last updated on 07/Feb/21 Commented by ajfour last updated on 07/Feb/21 $${Find}\:{radius}\:{of}\:{sphere}\:{of}\:{density} \\ $$$$\rho\:{that}\:{receives}\:{maximum} \\ $$$${normal}\:{reaction}\:{from}\:{wall}. \\ $$ Answered by…
Question Number 66194 by aliesam last updated on 10/Aug/19 $$\int\frac{{x}^{{a}} }{{bx}^{{n}} +{c}}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 658 by 123456 last updated on 22/Feb/15 $${proof}\:{that}\:{n}!>\left(\frac{{n}}{\mathrm{3}}\right)^{{n}} ,{n}\in\mathbb{N}^{\ast} \\ $$ Commented by 123456 last updated on 20/Feb/15 $${n}=\mathrm{1}\Rightarrow\mathrm{1}!=\mathrm{1}>\frac{\mathrm{1}}{\mathrm{3}}=\left(\frac{\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{1}} \\ $$$${n}=\mathrm{1}\Rightarrow\mathrm{0}!=\mathrm{1}>\frac{\mathrm{1}}{\mathrm{3}}\approx\mathrm{0}.\mathrm{33} \\ $$$${n}=\mathrm{2}\Rightarrow\mathrm{2}!=\mathrm{2}>\frac{\mathrm{4}}{\mathrm{9}}=\left(\frac{\mathrm{2}}{\mathrm{3}}\right)^{\mathrm{2}}…
Question Number 657 by 123456 last updated on 21/Feb/15 $${if}\:\left({a}_{{n}} \right)\:{and}\:\left({b}_{{n}} \right)\:{are}\:{two}\:{real}\:{sequence} \\ $$$${such}\:{that}\:{e}^{{a}_{{n}} } ={a}_{{n}} +{e}^{{b}_{{n}} } \\ $$$$\left.{a}\right)\:{proof}\:{that}\:{a}_{{n}} >\mathrm{0}\Rightarrow{b}_{{n}} >\mathrm{0} \\ $$$$\left.{b}\right)\:{if}\:{a}_{{n}} >\mathrm{0}\forall{n}\in\mathbb{N}\:{if}\:\underset{{n}=\mathrm{0}}…
Question Number 655 by 123456 last updated on 19/Feb/15 $${f}\left({z}\right)=\frac{\mathrm{1}−\frac{\mathrm{1}−{z}^{\mathrm{2}} }{\mathrm{2}+{z}^{\mathrm{2}} }}{\mathrm{2}+\frac{\mathrm{1}−{z}^{\mathrm{2}} }{\mathrm{2}+{z}^{\mathrm{2}} }} \\ $$$$\frac{{f}\left(\mathrm{0}\right)+{f}\left(\mathrm{1}\right)}{\mathrm{2}}−{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)=? \\ $$ Answered by prakash jain last updated on…
Question Number 652 by 123456 last updated on 19/Feb/15 $${if}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:{is}\:{continuous}\:{and} \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right)+{y} \\ $$$$\mathrm{1}.\:{find}\:{f}\left({x}\right) \\ $$$$\mathrm{2}.\:{proof}\:{or}\:{disproof}\:{that}\:{f}'\left({x}\right)=\mathrm{1} \\ $$$$\mathrm{3}.\:{if}\:{f}\left(\mathrm{0}\right)=\mathrm{0}\:{proof}\:{or}\:{disproof}\:{that}\:{f}\left({x}\right)={x} \\ $$ Answered by prakash jain last…
Question Number 650 by 123456 last updated on 19/Feb/15 $${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right)+{f}\left({y}\right){g}\left({y}\right) \\ $$$${g}\left({x}+{y}\right)={f}\left({x}\right){g}\left({x}\right)+{g}\left({y}\right) \\ $$ Answered by prakash jain last updated on…
Question Number 66185 by Tony Lin last updated on 10/Aug/19 $$\left({e}^{\frac{\mathrm{1}}{{e}}} \right)^{\left({e}^{\frac{\mathrm{1}}{{e}}} \right)^{.\centerdot^{.\left({e}^{\frac{\mathrm{1}}{{e}}} \right)} } } =? \\ $$ Commented by GordonYeeman last updated on…
Question Number 131717 by LYKA last updated on 07/Feb/21 $${the}\:{temperature}\:{of}\:{a}\:{fluid} \\ $$$${in}\:{heating}\:{unit}\:{of}\:{a}\:{plant}\:{is}\:{given}\:{by} \\ $$$${T}\left({x}.{y}.{z}\right)=\:\frac{\mathrm{100}\left({z}−\mathrm{3}\right)}{\mathrm{10}−\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\left({y}−\mathrm{2}\right)^{\mathrm{2}} } \\ $$$${find}\:{the}\:{minimum}\:{and}\:{maximum}\: \\ $$$${temperatures}\:{if}\:{the}\:{heat}\:{exchanging}\: \\ $$$${components}\:{have}\:{the}\:{shapes}\: \\ $$$${z}=\frac{{x}^{\mathrm{2}} }{\mathrm{4}}−\frac{{y}^{\mathrm{2}}…
Question Number 647 by 123456 last updated on 18/Feb/15 $$\mathrm{log}_{{x}} \left({y}^{\pi} \right)+\mathrm{log}_{{y}} \left({x}^{{e}} \right)={a} \\ $$$$\frac{\mathrm{1}}{\mathrm{log}_{{y}} \left({x}^{\pi^{−\mathrm{1}} } \right)}−\frac{\mathrm{1}}{\mathrm{log}_{{x}} \left({y}^{{e}^{−\mathrm{1}} } \right)}={b} \\ $$$$\frac{{x}^{{a}+{b}+\mathrm{2}{e}} }{{y}^{{a}−{b}+\mathrm{2}\pi}…