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Author: Tinku Tara

Question-210396

Question Number 210396 by jirodomo last updated on 08/Aug/24 Commented by jirodomo last updated on 08/Aug/24 $$\mathrm{applying}\:\mathrm{partial}\:\mathrm{fraction}\:\mathrm{decomposition} \\ $$$$\mathrm{straight}\:\mathrm{away}\:\mathrm{seems}\:\mathrm{impossible}\:\mathrm{here}. \\ $$$$\mathrm{is}\:\mathrm{there}\:\mathrm{other}\:\mathrm{way}?\:\mathrm{im}\:\mathrm{stuck}\:\mathrm{for}\:\mathrm{a}\:\mathrm{few} \\ $$$$\mathrm{months}\:\mathrm{now}. \\ $$…

If-the-roots-of-the-quadratic-equation-a-b-c-x-2-c-b-a-x-2-b-c-0-are-real-and-equal-then-find-a-b-c-

Question Number 210362 by MATHEMATICSAM last updated on 10/Sep/24 $$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{quadratic}\:\mathrm{equation} \\ $$$$\left({a}\:−\:{b}\:+\:{c}\right){x}^{\mathrm{2}} \:+\:\left({c}\:−\:{b}\:−\:{a}\right){x}\:+\:\mathrm{2}\left({b}\:−\:{c}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{are}\:\mathrm{real}\:\mathrm{and}\:\mathrm{equal}\:\mathrm{then}\:\mathrm{find}\:\frac{{a}}{{b}\:−\:{c}}\:. \\ $$ Commented by som(math1967) last updated on 08/Aug/24 $${not}\:{qudratic}\:,{it}\:{should}\:{be}\:\left({a}−{b}+{c}\right){x}^{\mathrm{2}}…

Question-210390

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-210416

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…

0-x-1-x-2-1-x-dx-

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-210355

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}}…