Question Number 210356 by hardmath last updated on 08/Aug/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 210421 by ajfour last updated on 08/Aug/24 Answered by mr W last updated on 08/Aug/24 Commented by mr W last updated on 08/Aug/24…
Question Number 210390 by hardmath last updated on 08/Aug/24 Answered by Berbere last updated on 08/Aug/24 $${t}\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{{t}}\right)={f}\left({t}\right) \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}{f}\left({x}\right)=\mathrm{1}\Rightarrow\exists{M}\in\mathbb{R}_{+} \:\forall{x}\geqslant{M}\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\leqslant{f}\left({x}\right)\leqslant\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\Rightarrow\forall{x}\geqslant{M} \\…
Question Number 210416 by Adeyemi889 last updated on 08/Aug/24 Commented by Adeyemi889 last updated on 08/Aug/24 $$\boldsymbol{{pls}}\:\boldsymbol{{someone}}\:\boldsymbol{{should}}\:\boldsymbol{{help}}\:\boldsymbol{{me}}\:\boldsymbol{{with}}\:\boldsymbol{{this}}\:\boldsymbol{{partail}}\:\boldsymbol{{fraction}}\: \\ $$$$\boldsymbol{{its}}\:\boldsymbol{{an}}\:\boldsymbol{{assignment}}\:\boldsymbol{{plss}}\:\boldsymbol{{help}}\:\boldsymbol{{me}}\: \\ $$ Commented by mr W…
Question Number 210354 by klipto last updated on 08/Aug/24 $$\int_{\mathrm{0}} ^{\boldsymbol{\alpha}} \frac{\boldsymbol{\mathrm{x}}}{\left(\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} \right)\left(\mathrm{1}+\boldsymbol{\alpha\mathrm{x}}\right)}\boldsymbol{\mathrm{dx}} \\ $$ Answered by klipto last updated on 08/Aug/24 $$ \\ $$…
Question Number 210355 by hardmath last updated on 08/Aug/24 Answered by Berbere last updated on 08/Aug/24 $${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +\gamma{ab}\overset{{AM}−{GM}} {\leqslant}\left(\frac{\gamma}{\mathrm{2}}+\mathrm{1}\right)\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right);\gamma>\mathrm{0} \\ $$$$\frac{{a}^{\mathrm{3}} +{b}^{\mathrm{3}}…
Question Number 210372 by Spillover last updated on 08/Aug/24 Commented by Frix last updated on 08/Aug/24 $$\mathrm{I}\:\mathrm{get}\:\pi^{\mathrm{2}} \\ $$ Answered by Berbere last updated on…
Question Number 210373 by Spillover last updated on 08/Aug/24 Commented by Frix last updated on 08/Aug/24 $$\mathrm{I}\:\mathrm{get}\:\mathrm{2ln}\:\mathrm{3} \\ $$ Commented by Spillover last updated on…
Question Number 210374 by Spillover last updated on 08/Aug/24 Commented by Frix last updated on 08/Aug/24 $$=\mathrm{Li}_{\mathrm{1000}} \:\left(\mathrm{1}\right) \\ $$$$\mathrm{Better}\:\mathrm{question}: \\ $$$$\mathrm{Show}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{{n}!}\underset{\mathrm{0}} {\overset{\infty}…
Question Number 210375 by Spillover last updated on 08/Aug/24 Commented by som(math1967) last updated on 08/Aug/24 $$\:\boldsymbol{{if}}\:\mathrm{sin}^{−\mathrm{1}} \boldsymbol{{x}}+\mathrm{sin}^{−\mathrm{1}} \boldsymbol{{y}}+\mathrm{sin}^{−\mathrm{1}} \boldsymbol{{z}}=\boldsymbol{\pi} \\ $$$${then}\:{x}^{\mathrm{4}} +{y}^{\mathrm{4}} +{z}^{\mathrm{4}} +\mathrm{4}\boldsymbol{{x}}^{\mathrm{2}}…