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Author: Tinku Tara

Solve-the-following-compound-inequation-in-interval-0-2pi-tan-x-2-1-and-tan-x-2-lt-0-

Question Number 1418 by Rasheed Ahmad last updated on 04/Aug/15 $${Solve}\:{the}\:{following}\:{compound} \\ $$$${inequation}\:{in}\:{interval}\:\left(\mathrm{0},\:\mathrm{2}\pi\right), \\ $$$${tan}\frac{{x}}{\mathrm{2}}\:\leqslant\:−\mathrm{1}\:\:{and}\:\:{tan}\frac{{x}}{\mathrm{2}}\:<\:\mathrm{0}\:. \\ $$ Commented by 123456 last updated on 31/Jul/15 $$\mathrm{tan}\:\frac{\pi}{\mathrm{4}}=−\mathrm{tan}\:\frac{\mathrm{3}\pi}{\mathrm{4}}=\mathrm{tan}\:\frac{\mathrm{5}\pi}{\mathrm{4}}=−\mathrm{tan}\:\frac{\mathrm{7}\pi}{\mathrm{4}}=\mathrm{1}…

sin-sin-x-cos-cos-x-x-0-2pi-

Question Number 1417 by 123456 last updated on 30/Jul/15 $$\mathrm{sin}\:\left(\mathrm{sin}\:{x}\right)\leqslant\mathrm{cos}\:\left(\mathrm{cos}\:{x}\right) \\ $$$${x}\in\left[\mathrm{0},\mathrm{2}\pi\right) \\ $$ Commented by Rasheed Ahmad last updated on 02/Aug/15 $${What}\:{to}\:{do}\:{with}\:{it}?\:{Is}\:{it}\:{an}\:{inequation} \\ $$$${to}\:{solve}?\:{Or}\:{is}\:{it}\:{an}\:{identity}\:{to}…

define-f-x-y-xy-x-2-y-2-x-2-y-2-if-x-y-0-0-0-if-x-y-0-0-show-that-f-f-x-and-f-y-are-continuous-on-R-2-show-that-2-f-x-y-and-

Question Number 132477 by KZ last updated on 14/Feb/21 $${define} \\ $$$${f}\left({x}.{y}\right)= \\ $$$$\left.\left\{\frac{\mathrm{xy}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \right)\:}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:{if}\:\left({x}.{y}\right)\neq\right)\mathrm{0}.\mathrm{0}\right) \\ $$$$\:\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{if}\:\left({x}.{y}\right)=\left(\mathrm{0}.\mathrm{0}\right) \\ $$$$ \\ $$$${show}\:{that}\:{f},\frac{\partial{f}}{\partial{x}}\:{and}\:\frac{\partial{f}}{\partial{y}\:\:}\:{are}\: \\…

Solve-the-following-inequality-sinx-1-cosx-1-where-0-x-lt-2pi-cosx-0-

Question Number 1407 by 112358 last updated on 29/Jul/15 $${Solve}\:{the}\:{following}\:{inequality} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{sinx}+\mathrm{1}}{{cosx}}\leqslant\mathrm{1} \\ $$$${where}\:\mathrm{0}\leqslant{x}<\mathrm{2}\pi\:,\:{cosx}\neq\mathrm{0} \\ $$ Commented by 123456 last updated on 29/Jul/15 $${f}\left({x}\right)=\frac{\mathrm{sin}\:{x}+\mathrm{1}}{\mathrm{cos}\:{x}} \\…

x-cosh-x-sinh-x-2-dx-

Question Number 132473 by physicstutes last updated on 14/Feb/21 $$\int\:\frac{{x}\:\mathrm{cosh}\:{x}}{\left(\mathrm{sinh}\:{x}\right)^{\mathrm{2}} }\:{dx} \\ $$ Answered by mathmax by abdo last updated on 14/Feb/21 $$\mathrm{I}=\int\:\frac{\mathrm{xchx}}{\mathrm{sh}^{\mathrm{2}} \mathrm{x}}\mathrm{dx}\:\:\mathrm{by}\:\mathrm{parts}\:\:\mathrm{u}^{'} \:=\frac{\mathrm{chx}}{\mathrm{sh}^{\mathrm{2}}…

Question-66938

Question Number 66938 by Cmr 237 last updated on 20/Aug/19 Commented by mathmax by abdo last updated on 21/Aug/19 $$\left.\mathrm{8}\right){by}\:{parts}\:\:\int\:{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right){dx}\:={xln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)−\int\:{x}\frac{\mathrm{2}{x}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$={xln}\left(\mathrm{1}+{x}^{\mathrm{2}}…