Question Number 152889 by SANOGO last updated on 02/Sep/21 $$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}^{\alpha} }{\left({n}+\mathrm{1}\right)^{\alpha} \:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\mathrm{1}+{n}\alpha\right)}=\frac{\mathrm{1}}{\mathrm{6}{o}}\: \\ $$$$\alpha=? \\ $$$$\alpha=?{q} \\ $$ Commented…
Question Number 152887 by otchereabdullai@gmail.com last updated on 02/Sep/21 $$\int_{\mathrm{1}} ^{\:\mathrm{2}} \:\:\frac{\mathrm{3}}{\:\sqrt{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{3}} }} \\ $$ Answered by Ar Brandon last updated on 02/Sep/21 $${I}=\int_{\mathrm{1}}…
Question Number 152879 by SANOGO last updated on 02/Sep/21 $$\underset{{x}\rightarrow+{oo}} {\mathrm{lim}}\frac{\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}^{\alpha} \:\:\:}{\left({n}+\mathrm{1}\right)^{\alpha} \:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left({n}\alpha+\mathrm{1}\right)}=\frac{\mathrm{1}}{\mathrm{6}{o}}\:\:.\alpha=? \\ $$ Commented by talminator2856791 last updated on…
Question Number 87335 by naka3546 last updated on 04/Apr/20 Answered by TANMAY PANACEA. last updated on 04/Apr/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{sin}^{{a}} {x}}{{sin}^{{a}} {x}+{cos}^{{a}} {x}}{dx}=\frac{{I}\pi}{\mathrm{4}} \\ $$$${using}\:\int_{\mathrm{0}}…
Question Number 152856 by Olaf_Thorendsen last updated on 02/Sep/21 $$\mathrm{Monsieur}\:\mathrm{Puissant},\:\mathrm{je}\:\mathrm{quitte}\:\mathrm{ce}\:\mathrm{forum} \\ $$$$\mathrm{math}\acute {\mathrm{e}matique}\:\mathrm{d}\acute {\mathrm{e}finitivement}\:\mathrm{mais} \\ $$$$\mathrm{sans}\:\mathrm{avoir}\:\mathrm{dit}\:\mathrm{que}\:\mathrm{j}'\mathrm{ai}\:\mathrm{ador}\acute {\mathrm{e}}\:\acute {\mathrm{e}changer} \\ $$$$\mathrm{avec}\:\mathrm{vous}. \\ $$$$ \\ $$$$\mathrm{Bonne}\:\mathrm{continuation}\:\mathrm{et}\:\mathrm{vive}\:\mathrm{les} \\…
Question Number 152848 by 0731619 last updated on 02/Sep/21 Commented by hknkrc46 last updated on 02/Sep/21 $$\boldsymbol{{Wrong}}\:!!! \\ $$$$\sqrt{\mathrm{12}}\:+\:\cancel{\sqrt{\mathrm{18}}}\:\rightarrow\:\sqrt{\mathrm{12}}\:+\:\sqrt{\mathrm{16}} \\ $$ Commented by hknkrc46 last…
Question Number 152841 by 0731619 last updated on 02/Sep/21 Answered by bobhans last updated on 02/Sep/21 $$\left(\mathrm{2}\right)\frac{\mathrm{1}}{\mathrm{4}}\int\:\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{2}{x}\right)\:{dx}\:= \\ $$$$\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{4}}\int\:\frac{\mathrm{1}−\mathrm{cos}\:\left(\mathrm{4}{x}\right)}{\mathrm{2}}\:{dx}\:= \\ $$$$\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{4}}\left(\frac{{x}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{8}}\mathrm{sin}\:\left(\mathrm{4}{x}\right)\right)+\:{c}\:= \\ $$$$\:\:\:\:\:\frac{{x}}{\mathrm{8}}−\frac{\mathrm{sin}\:\left(\mathrm{4}{x}\right)}{\mathrm{32}}\:+\:{c} \\…
Question Number 152817 by rexford last updated on 01/Sep/21 $$ \\ $$$${Find}\:{the}\:{coefficient}\:{of} \\ $$$$\mathrm{1}.{x}^{\mathrm{20}\:} {in}\:\left(\mathrm{1}−{x}+{x}^{\mathrm{2}} \right)^{\mathrm{20}} \\ $$$$ \\ $$$$\mathrm{2}.{x}^{\mathrm{4}} \:{in}\:\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} \right)_{} ^{\mathrm{11}} \\…
Question Number 152805 by mathlove last updated on 01/Sep/21 Answered by MJS_new last updated on 01/Sep/21 $${x}\geqslant\mathrm{0} \\ $$$$\mathrm{3ln}\:\mathrm{2}\:{x}=\mathrm{7ln}\:\mathrm{2}\:\sqrt{{x}} \\ $$$$\mathrm{3}{x}=\mathrm{7}\sqrt{{x}} \\ $$$${x}=\mathrm{0}\vee{x}=\frac{\mathrm{49}}{\mathrm{9}} \\ $$…
Question Number 152801 by SANOGO last updated on 01/Sep/21 $${resouds} \\ $$$$\mid\mathrm{1}−{x}\mid{y}'+{xy}={x} \\ $$ Commented by mathmax by abdo last updated on 02/Sep/21 $$\mathrm{case}\:\mathrm{1}\:\:\mathrm{if}\:\mathrm{x}>\mathrm{1}\:\:\:\mathrm{e}\:\Rightarrow\left(\mathrm{x}−\mathrm{1}\right)\mathrm{y}^{,} \:+\mathrm{xy}=\mathrm{x}\:\:\left(\mathrm{e}\right)…