Question Number 107447 by mathdave last updated on 10/Aug/20 Commented by mathmax by abdo last updated on 10/Aug/20 $$\mathrm{what}\:\mathrm{mean}\:\mathrm{G}\:? \\ $$ Commented by mathdave last…
Question Number 41911 by lucha116 last updated on 15/Aug/18 $${h}\left({x}\right)=\sqrt{{sin}^{\mathrm{4}} {x}+{cos}^{\mathrm{4}} {x}−\mathrm{2}{msinxcosx}} \\ $$$${Find}\:{all}\:{the}\:{values}\:{of}\:{the}\:{parameter}\:{m}\:{for}\:{the}\:{funtion}\:{denined}\:{on}\:{R} \\ $$$$ \\ $$ Commented by MJS last updated on 15/Aug/18…
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Question Number 41895 by lucha116 last updated on 15/Aug/18 $$\sqrt{\mathrm{3}}{sin}\mathrm{3}{x}−{cos}\mathrm{3}{x}+\mathrm{2}{sin}\frac{\mathrm{9}{x}}{\mathrm{4}}=\mathrm{4} \\ $$ Commented by MJS last updated on 15/Aug/18 $$\mathrm{the}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{this}\:\mathrm{question}\:\mathrm{is}\:\mathrm{included}\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{former}\:\mathrm{similar}\:\mathrm{one}.\:\mathrm{there}\:\mathrm{the}\:\mathrm{maximum} \\ $$$$\mathrm{was}\:\begin{pmatrix}{\frac{\mathrm{2}\pi}{\mathrm{9}}+\frac{\mathrm{8}\pi}{\mathrm{3}}{z}}\\{\mathrm{2}}\end{pmatrix}\:\mathrm{with}\:{z}\in\mathbb{Z},\:\mathrm{here}\:\mathrm{it}'\mathrm{s}\:\mathrm{the}\:\mathrm{zeros} \\…
Question Number 107428 by abony1303 last updated on 10/Aug/20 $$\mathrm{The}\:\mathrm{polynomial}\:{P}\left({x}\right)=\mathrm{x}^{\mathrm{3}} +\mathrm{ax}^{\mathrm{2}} −\mathrm{4x}+\mathrm{b}, \\ $$$$\mathrm{where}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{are}\:\mathrm{constants}.\:\mathrm{Given}\:\mathrm{that} \\ $$$$\mathrm{x}−\mathrm{2}\:\mathrm{is}\:\mathrm{a}\:\mathrm{factor}\:\mathrm{of}\:{P}\left({x}\right)\:\mathrm{and}\:\mathrm{that}\:\mathrm{a}\:\mathrm{remainder} \\ $$$$\mathrm{of}\:\mathrm{6}\:\mathrm{is}\:\mathrm{obtained}\:\mathrm{when}\:{P}\left({x}\right)\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by} \\ $$$$\left(\mathrm{x}+\mathrm{1}\right),\:\mathrm{find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}. \\ $$ Commented by abony1303…
Question Number 107419 by DeepakMahato last updated on 10/Aug/20 $${Factorize}:−\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{2}\sqrt{\mathrm{5}}\boldsymbol{{x}}+\mathrm{3} \\ $$$$ \\ $$$$ \\ $$ Answered by nimnim last updated on 10/Aug/20 $${x}^{\mathrm{2}}…
Question Number 41878 by lucha116 last updated on 14/Aug/18 $$\sqrt{\mathrm{3}}{sin}\mathrm{3}{x}−{cos}\mathrm{3}{x}+\mathrm{2}{sin}\frac{\mathrm{9}{x}}{\mathrm{4}}=\mathrm{2} \\ $$ Answered by MJS last updated on 15/Aug/18 $${f}\left({x}\right)=\sqrt{\mathrm{3}}\mathrm{sin}\:\mathrm{3}{x}\:−\mathrm{cos}\:\mathrm{3}{x}\:+\mathrm{2sin}\:\frac{\mathrm{9}{x}}{\mathrm{4}}\:−\mathrm{2} \\ $$$$\mathrm{found}\:\mathrm{by}\:\mathrm{approximation}: \\ $$$$\mathrm{max}\left({f}\left({x}\right)\right)=\begin{pmatrix}{\frac{\mathrm{2}\pi}{\mathrm{9}}+\frac{\mathrm{8}\pi}{\mathrm{3}}{n}}\\{\mathrm{2}}\end{pmatrix}\:\mathrm{with}\:{n}\in\mathbb{Z} \\…
Question Number 172910 by DAVONG last updated on 03/Jul/22 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{e}−\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{x}−\mathrm{1}}} }{\mathrm{x}−\mathrm{1}}=? \\ $$ Answered by FongXD last updated on 03/Jul/22 $$\mathrm{L}=\underset{\mathrm{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{e}−\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{x}−\mathrm{1}}\mathrm{lnx}} }{\mathrm{x}−\mathrm{1}}=−\underset{\mathrm{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{e}\left(\mathrm{e}^{\frac{\mathrm{lnx}}{\mathrm{x}−\mathrm{1}}−\mathrm{1}}…