Question Number 144261 by ZiYangLee last updated on 23/Jun/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{k}={n}} {\overset{\mathrm{2}{n}} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}}. \\ $$ Commented by Dwaipayan Shikari last updated on 23/Jun/21 $$\underset{{n}\rightarrow\infty}…
Question Number 144260 by ZiYangLee last updated on 23/Jun/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{real}\:\mathrm{number} \\ $$$${x}\:\mathrm{that}\:\mathrm{satisfy}\:\left(\mathrm{2}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{1}\right)^{\mathrm{2}{x}−\mathrm{3}} =\mathrm{1} \\ $$ Answered by Ar Brandon last updated on 24/Jun/21 $$\mathrm{2x}−\mathrm{3}=\mathrm{0}\:\vee\:\mathrm{2x}^{\mathrm{2}}…
Question Number 144244 by SOMEDAVONG last updated on 23/Jun/21 $$\mathrm{I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{5tan}^{\mathrm{4}} \mathrm{x}+\mathrm{3cot}^{\mathrm{4}} \mathrm{x}}{\mathrm{tan}^{\mathrm{4}} \mathrm{x}+\mathrm{cot}^{\mathrm{4}} \mathrm{x}}\mathrm{dx}=? \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 144246 by SOMEDAVONG last updated on 23/Jun/21 $$\mathrm{A}=\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}}\left[\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} +\mathrm{3}\left(\mathrm{1}\right)+\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} +\mathrm{3}\left(\mathrm{2}\right)+\mathrm{2}}\:+..+\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} +\mathrm{3n}+\mathrm{2}}\right] \\ $$ Answered by Ar Brandon last updated on 23/Jun/21 $$\mathscr{L}=\underset{\mathrm{n}\rightarrow\infty}…
Question Number 144174 by lapache last updated on 22/Jun/21 $$\int_{\mathrm{0}} ^{\pi} \left({sinx}\right)^{\mathrm{2}{n}} {dx}=….?\:\:\:\forall{n}\in\mathbb{N} \\ $$ Commented by Willson last updated on 22/Jun/21 $$\mathrm{4}^{\mathrm{n}} \mathrm{sin}^{\mathrm{2n}} \mathrm{t}\:=\:\mathrm{C}_{\mathrm{2n}}…
Question Number 78628 by naka3546 last updated on 19/Jan/20 $${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}}…