Question Number 78628 by naka3546 last updated on 19/Jan/20 $${Find}\:\:{minimum}\:\:{value}\:\:{of} \\ $$$$\:\:\:\:\:\:\:{y}\:\:=\:\:\frac{\mathrm{2}{x}}{{x}^{\mathrm{2}} \:+\:{x}\:+\:\mathrm{1}} \\ $$$${x}\:,\:{y}\:\:\in\:\:\mathbb{R} \\ $$$${Without}\:\:{Differential} \\ $$ Commented by john santu last updated…
Question Number 144152 by SOMEDAVONG last updated on 22/Jun/21 $$\mathrm{I}=\int\frac{\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } +\mathrm{e}^{\mathrm{x}} }{\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } +\mathrm{1}}\mathrm{dx}=? \\ $$ Answered by ArielVyny last updated on 22/Jun/21 $$=\int\frac{{e}^{{x}^{\mathrm{2}}…
Question Number 13059 by sandy_suhendra last updated on 12/May/17 $$\mathrm{please}\:\mathrm{help}\:\mathrm{for} \\ $$$$\int_{−\mathrm{3}\pi\:} ^{\:\:\:\mathrm{3}\pi} \mathrm{sin}^{\mathrm{2009}} \mathrm{x}\:\mathrm{dx} \\ $$ Answered by mrW1 last updated on 12/May/17 $${if}\:{f}\left(−{x}\right)=−{f}\left({x}\right),\:{then}…
Question Number 144107 by SOMEDAVONG last updated on 21/Jun/21 $$\mathrm{A}=\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}}\frac{\mathrm{1}+\sqrt[{\mathrm{7}}]{\mathrm{2}}+\sqrt[{\mathrm{7}}]{\mathrm{3}}+\sqrt[{\mathrm{7}}]{\mathrm{4}}+…..+\sqrt[{\mathrm{7}}]{\mathrm{n}}}{\:\sqrt[{\mathrm{7}}]{\mathrm{n}^{\mathrm{9}} }}\:=? \\ $$ Answered by Dwaipayan Shikari last updated on 21/Jun/21 $${A}=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}+\sqrt[{\mathrm{7}}]{\mathrm{2}}+..+\sqrt[{\mathrm{7}}]{{n}}}{\:\sqrt[{\mathrm{7}}]{{n}^{\mathrm{8}} }}…
Question Number 13030 by 2002154006 last updated on 11/May/17 Commented by prakash jain last updated on 12/May/17 $${x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{5}=\mathrm{0} \\ $$$$\mathrm{x}_{\mathrm{1}} +\mathrm{x}_{\mathrm{2}} =\mathrm{4} \\ $$$$\mathrm{x}_{\mathrm{1}}…
Question Number 144094 by mohammad17 last updated on 21/Jun/21 Commented by mohammad17 last updated on 21/Jun/21 $${help}\:{me}\:{sir}\:{please} \\ $$ Answered by Olaf_Thorendsen last updated on…
Question Number 144085 by mohammad17 last updated on 21/Jun/21 Commented by mohammad17 last updated on 21/Jun/21 $${help}\:{me}\:{sir} \\ $$ Answered by mathmax by abdo last…
Question Number 144084 by Rankut last updated on 21/Jun/21 $${if}\:\:{a}+\frac{\mathrm{1}}{{a}}=−\mathrm{1} \\ $$$$\:{a}^{\mathrm{1234567891011}} +\frac{\mathrm{1}}{{a}^{\mathrm{1110987654321}} }=?? \\ $$$$ \\ $$ Answered by MJS_new last updated on 21/Jun/21…
Question Number 65961 by mmkkmm000m last updated on 06/Aug/19 $$\mathrm{Let}\:\frac{{d}}{{dx}}\left({F}\left({x}\right)\right)\:=\:\frac{{e}^{\mathrm{sin}\:{x}} }{{x}}\:,\:{x}>\mathrm{0}. \\ $$$$\mathrm{If}\:\underset{\:\mathrm{1}} {\overset{\mathrm{4}} {\int}}\:\:\frac{\mathrm{2}\:{e}^{\mathrm{sin}\:{x}^{\mathrm{2}} } }{{x}}\:{dx}\:=\:{F}\left({k}\right)−{F}\left(\mathrm{1}\right),\:\mathrm{then}\:\mathrm{one} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\:{k}\:\:\mathrm{is} \\ $$ Answered by mr W…
Question Number 131429 by mathlove last updated on 04/Feb/21 $${if}\:\:\:\:\frac{{aa}−{bb}}{{ab}+{ba}}=\frac{\mathrm{1}}{\mathrm{7}}\:\:\:\:\:\:\:\:\:{then}\:{faind}\:\frac{{a}}{{b}}=? \\ $$ Answered by Dwaipayan Shikari last updated on 04/Feb/21 $$\frac{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }{\mathrm{2}{ab}}=\frac{\mathrm{1}}{\mathrm{7}}\Rightarrow\left(\frac{{a}}{{b}}\right)−\left(\frac{{b}}{{a}}\right)=\frac{\mathrm{2}}{\mathrm{7}}\Rightarrow\frac{{a}}{{b}}=\frac{−\frac{\mathrm{2}}{\mathrm{7}}\pm\sqrt{\frac{\mathrm{4}}{\mathrm{49}}+\mathrm{4}}}{\mathrm{2}} \\ $$$$=\frac{−\mathrm{1}\pm\mathrm{5}\sqrt{\mathrm{2}}}{\mathrm{7}}…