Category: Algebra

Question Number 210390 by hardmath last updated on 08/Aug/24 Answered by Berbere last updated on 08/Aug/24 $$t{\tan }^{-1}\left(\frac{1}{t}\right)=f\left(t\right)$$$$\underset{x\to \mathrm{\infty }}{\lim }f\left(x\right)=1\Rightarrow \mathrm{\exists }M\in {\mathbb{R}}_{+}\mathrm{\forall }x⩾M\frac{1}{2}⩽f\left(x\right)⩽\frac{3}{2}$$$$\Rightarrow\forall{x}\geqslant{M} \…

Question Number 210355 by hardmath last updated on 08/Aug/24 Answered by Berbere last updated on 08/Aug/24 $$a^2+b^2+\gamma ab\stackrel{AM-GM}{⩽}(\frac{\gamma }{2}+1)(a^2+b^2);\gamma >0$$$$\frac{{a}^{\mathrm{3}} +{b}^{\mathrm{3}}…

Question Number 210375 by Spillover last updated on 08/Aug/24 Commented by som(math1967) last updated on 08/Aug/24 $$\mathit{i}\mathit{f}{\sin }^{-1}\mathit{x}+{\sin }^{-1}\mathit{y}+{\sin }^{-1}\mathit{z}=\mathit{\pi }$$$${then}\:{x}^{\mathrm{4}} +{y}^{\mathrm{4}} +{z}^{\mathrm{4}} +\mathrm{4}\boldsymbol{{x}}^{\mathrm{2}}…

Question Number 210368 by peter frank last updated on 08/Aug/24 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 210318 by peter frank last updated on 06/Aug/24 Commented by mr W last updated on 06/Aug/24 $$whatshouldbereachedwiththe$$$$singletubewhenitreplacesthethree$$$$ones?thesameflowratewiththe$$$${single}\:{tube}\:{as}\:{with}\:{the}\:{three}\:{tubes}?…