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Author: Tinku Tara

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Question Number 137055 by mathmax by abdo last updated on 29/Mar/21 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{\mathrm{dx}}{\left(\mathrm{1}+\mathrm{cosx}\:+\mathrm{3sinx}\right)^{\mathrm{2}} } \\ $$ Commented by MJS_new last updated on 30/Mar/21 $$\mathrm{0}\leqslant\left(\mathrm{1}+\mathrm{cos}\:{x}\:+\mathrm{3sin}\:{x}\right)^{\mathrm{2}}…

Question-71517

Question Number 71517 by TawaTawa last updated on 16/Oct/19 Answered by mind is power last updated on 16/Oct/19 $$\mathrm{AD}=\mathrm{x} \\ $$$$\frac{\mathrm{x}}{\mathrm{sin}\left(\theta\right)}=\frac{\mathrm{DC}}{\mathrm{sin}\left(\theta\right)}\Rightarrow\mathrm{1}=\frac{\mathrm{x}}{\mathrm{DC}} \\ $$$$\frac{\mathrm{x}}{\mathrm{sin}\left(\mathrm{3}\theta\right)}=\frac{\mathrm{DC}}{\mathrm{sin}\left(\mathrm{10}\theta\right)}\Rightarrow\frac{\mathrm{x}}{\mathrm{DC}}=\frac{\mathrm{sin}\left(\mathrm{3}\theta\right)}{\mathrm{sin}\left(\mathrm{10}\theta\right)} \\ $$$$…

f-1-f-1-0-Is-this-true-When-is-this-not-true-

Question Number 5978 by FilupSmith last updated on 08/Jun/16 $${f}\left(\mathrm{1}\right){f}\left(−\mathrm{1}\right)\leqslant\mathrm{0} \\ $$$$\mathrm{Is}\:\mathrm{this}\:\mathrm{true}? \\ $$$$\mathrm{When}\:\mathrm{is}\:\mathrm{this}\:\mathrm{not}\:\mathrm{true}? \\ $$ Commented by Yozzii last updated on 09/Jun/16 $${If}\:{x}\in\mathbb{R},\:{f}\left({x}\right)\in\mathbb{R}\:{is}\:{odd}\:\Rightarrow{f}\left({x}\right){f}\left(−{x}\right)=−\left({f}\left({x}\right)\right)^{\mathrm{2}} \leqslant\mathrm{0}…

Question-71513

Question Number 71513 by aliesam last updated on 16/Oct/19 Commented by kaivan.ahmadi last updated on 16/Oct/19 $$×\frac{\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}+\sqrt{{x}−\mathrm{1}}}{\:\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}+\sqrt{{x}−\mathrm{1}}}={lim}_{{x}\rightarrow+\infty} \frac{{x}^{\mathrm{2}} +\mathrm{2}}{\:\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}+\sqrt{{x}−\mathrm{1}}}= \\ $$$$\equiv{lim}_{{x}\rightarrow+\infty} \frac{{x}^{\mathrm{2}}…

montrer-que-a-b-R-ona-2-ab-a-2-b-2-Endeduire-que-x-1-x-n-R-on-a-i-1-n-x-i-2-n-i-1-n-x-i-2-please-i-need-help-

Question Number 71508 by Cmr 237 last updated on 16/Oct/19 $$\mathrm{montrer}\:\mathrm{que}:\forall\mathrm{a},\mathrm{b}\in\mathbb{R}\:\mathrm{ona} \\ $$$$\mathrm{2}\mid\mathrm{ab}\mid\leqslant\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} \\ $$$$\mathrm{Endeduire}\:\mathrm{que}\:\forall\mathrm{x}_{\mathrm{1}} ,…,\mathrm{x}_{\mathrm{n}} \in\mathbb{R}\:\mathrm{on}\:\mathrm{a}: \\ $$$$\left(\underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mid\mathrm{x}_{\mathrm{i}} \mid\right)^{\mathrm{2}} \leqslant\mathrm{n}\underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{n}}…