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Author: Tinku Tara

Question-196934

Question Number 196934 by Amidip last updated on 03/Sep/23 Answered by aleks041103 last updated on 04/Sep/23 $${M}\left({x},{y}\right){dx}+{N}\left({x},{y}\right){dy}=\mathrm{0} \\ $$$${if}\:\:\partial_{{y}} {M}=\partial_{{x}} {N},\:{then}\:\exists{F}\left({x},{y}\right): \\ $$$${M}\left({x},{y}\right){dx}+{N}\left({x},{y}\right){dy}={dF}=\mathrm{0}\Rightarrow{F}={const}. \\ $$$${in}\:{our}\:{case}\:\partial_{{y}}…

Question-196929

Question Number 196929 by Amidip last updated on 03/Sep/23 Answered by som(math1967) last updated on 03/Sep/23 $$\mathrm{2}{U}_{\mathrm{6}} −\mathrm{3}{U}_{\mathrm{4}} +\mathrm{1} \\ $$$$=\mathrm{2}\left({sin}^{\mathrm{6}} \alpha+{cos}^{\mathrm{6}} \alpha\right)−\mathrm{3}\left({sin}^{\mathrm{4}} \alpha+{cos}^{\mathrm{4}} \right)+\mathrm{1}…

Question-196914

Question Number 196914 by SANOGO last updated on 03/Sep/23 Answered by witcher3 last updated on 03/Sep/23 $$−\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}>−\frac{\mathrm{1}}{\mathrm{n}} \\ $$$$\mathrm{I}_{\mathrm{n}} =\left[−\frac{\mathrm{1}}{\mathrm{n}},\mathrm{1}\right] \\ $$$$\mathrm{I}_{\mathrm{n}+\mathrm{1}} \:\:\subseteq\mathrm{I}_{\mathrm{n}} \:\:\mathrm{suite}\:\mathrm{decroissante}\:\mathrm{minore} \\…

Question-196893

Question Number 196893 by hardmath last updated on 02/Sep/23 Answered by Rasheed.Sindhi last updated on 02/Sep/23 $${x}=\sqrt{\left(−\mathrm{1}+{i}\right)+\sqrt{\left(−\mathrm{1}+{i}\right)+\sqrt{…}}}\: \\ $$$${x}=\sqrt{\left(−\mathrm{1}+{i}\right)+{x}}\: \\ $$$${x}^{\mathrm{2}} =\:\left(−\mathrm{1}+{i}\right)+{x} \\ $$$${x}^{\mathrm{2}} −{x}+\mathrm{1}−{i}=\mathrm{0}…