Question Number 17595 by virus last updated on 08/Jul/17 $${Let}\:{a},{b},{c}\:{be}\:{the}\:{posetive}\:{integer}\:{such}\:{that}\: \\ $$$${b}/{a}\:{is}\:{an}\:{also}\:{integer}\:{if}\:{a},{b},{c}\:{are}\:{in}\:{GP}\:{and}\: \\ $$$${AM}\:{of}\:{a},{b},{c}\:{is}\left({b}+\mathrm{2}\right)\:{then}\:{find}\:{the}\:{value}\:{of} \\ $$$$\left({a}^{\mathrm{2}} +{a}−\mathrm{14}\right)/\left({a}+\mathrm{1}\right) \\ $$ Commented by virus last updated on…
Question Number 83131 by 09658867628 last updated on 28/Feb/20 $${y}=\boldsymbol{{x}}^{\mathrm{4ln}\:\boldsymbol{{x}}} \\ $$ Commented by mr W last updated on 28/Feb/20 $${dear}\:{sir}: \\ $$$${please}\:{stop}\:{posting}\:{the}\:{same}\:{questions} \\ $$$${more}\:{times}!\:{if}\:{it}\:{occurs}\:{by}\:{mistake},…
Question Number 83127 by jagoll last updated on 28/Feb/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{x}\sqrt{\mathrm{3}}\:+\mathrm{y}\: \\ $$$$\mathrm{if}\:\mathrm{x}^{\mathrm{2}} \:+\mathrm{y}^{\mathrm{2}} −\mathrm{xy}=\:\mathrm{3}\:? \\ $$ Answered by mr W last updated on 28/Feb/20 $${let}\:{u}=\sqrt{\mathrm{3}}{x}+{y}…
Question Number 83123 by M±th+et£s last updated on 28/Feb/20 $$\int\frac{\left({x}^{\mathrm{2}} −\mathrm{1}\right)}{\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\right)\left({x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{2}\right)}\:{dx} \\ $$ Commented by mathmax by abdo last updated on 28/Feb/20 $${A}\:=\int\:\:\frac{{x}^{\mathrm{2}}…
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Question Number 148655 by mathdanisur last updated on 29/Jul/21 $$\underset{\boldsymbol{{n}}\rightarrow\infty} {{lim}}\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\frac{{nx}}{\mathrm{1}\:+\:{n}^{\mathrm{2}} {x}^{\mathrm{4}} }\:{dx}\:=\:? \\ $$ Answered by ArielVyny last updated on 29/Jul/21 $${n}\int_{\mathrm{0}}…
Question Number 148654 by mathdanisur last updated on 29/Jul/21 $$\underset{{x}\rightarrow\mathrm{1}} {{lim}}\left(\frac{\mathrm{1}+{x}}{\mathrm{2}+{x}}\right)^{\frac{\mathrm{1}−\sqrt{\boldsymbol{{x}}}}{\mathrm{1}−\boldsymbol{{x}}}} \:=\:? \\ $$ Answered by ArielVyny last updated on 29/Jul/21 $${e}^{\frac{\mathrm{1}−\sqrt{{x}}}{\mathrm{1}−{x}}{ln}\left(\frac{\mathrm{1}+{x}}{\mathrm{2}+{x}}\right)} \:\:\:\:{posons}\:{t}={x}−\mathrm{1}\:\begin{cases}{{x}\rightarrow\mathrm{1}}\\{{t}\rightarrow\mathrm{0}}\end{cases} \\ $$$${e}^{\frac{\sqrt{{t}+\mathrm{1}}−\mathrm{1}}{{t}}{ln}\left(\frac{{t}+\mathrm{2}}{{t}+\mathrm{3}}\right)}…
Question Number 17580 by b.e.h.i.8.3.417@gmail.com last updated on 08/Jul/17 Commented by b.e.h.i.8.3.417@gmail.com last updated on 08/Jul/17 $${triangle}\:{ABC},{is}\:{given}\:{with}: \\ $$$${AB}={c},{BC}={a},{AC}={b} \\ $$$${red}\:\:{lines},{are}\:{perpendicular}\:{bisectors} \\ $$$${of}\:{sides}. \\ $$$$\left.\mathrm{1}\right){find}\:{radius}\:{of}\:{a}\:{circle}\:{that}\:{passes}…
Question Number 83115 by 09658867628 last updated on 28/Feb/20 $$\int\mathrm{cos}\:{xe}^{\mathrm{sin}\:{x}} {dx} \\ $$ Commented by niroj last updated on 28/Feb/20 $$ \\ $$$$\:\int\boldsymbol{\mathrm{cos}}\:\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{dx}} \\…
Question Number 17576 by chux last updated on 07/Jul/17 $$\mathrm{solve}\:\mathrm{the}\:\mathrm{equation} \\ $$$$ \\ $$$$\mathrm{x}^{\mathrm{y}} =\mathrm{y}^{\mathrm{x}} …….\left(\mathrm{1}\right) \\ $$$$ \\ $$$$\mathrm{x}^{\mathrm{2}} =\mathrm{y}^{\mathrm{3}} …….\left(\mathrm{2}\right) \\ $$ Answered…