Question Number 132497 by mathocean1 last updated on 14/Feb/21 $${a},\:{b}\:\in\:\mathbb{R}. \\ $$$${Given}\:{a}^{\mathrm{3}} +{b}^{\mathrm{3}} −{ab}+\mathrm{11}=\mathrm{0} \\ $$$${Show}\:{that}\:−\frac{\mathrm{7}}{\mathrm{3}}<{a}+{b}<−\mathrm{2} \\ $$ Answered by MJS_new last updated on 14/Feb/21…
Question Number 132496 by mathmax by abdo last updated on 14/Feb/21 $$\mathrm{calculateA}_{\mathrm{n}} =\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{2}} }\mathrm{cos}\left(\mathrm{n}\right)\:\mathrm{andB}_{\mathrm{n}} =\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{2}} }\mathrm{cos}\left(\frac{\mathrm{n}\pi}{\mathrm{3}}\right) \\ $$ Answered…
Question Number 1426 by tabrez8590@gmail last updated on 31/Jul/15 $${why}\:{we}\:{can}\:{not}\:{compare}\:{any}\:{tow}\:{complex}\:{number}\:\: \\ $$$${how}\:{a}\:{cmplex}\:{number}\:{is}\:{uses}\:{a}\:{complex}\:{number}\:{practically}\:{please}\:{giveanexample} \\ $$ Commented by Rasheed Ahmad last updated on 03/Aug/15 $${Things}\:{with}\:{respect}\:{to}\:{single}\: \\ $$$${characteristic}\:{are}\:{easy}\:{to}\:{compare}.…
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Question Number 132494 by mnjuly1970 last updated on 14/Feb/21 Commented by MJS_new last updated on 14/Feb/21 $$\mathrm{sharing}\:\mathrm{these}\:\mathrm{transformations} \\ $$$$\mathrm{we}\:\mathrm{have}\:\mathrm{to}\:\mathrm{check}\:\mathrm{all}\:\mathrm{solutions}!!! \\ $$$$ \\ $$$${a}^{\mathrm{1}/\mathrm{2}} +{b}^{\mathrm{1}/\mathrm{2}} ={c}^{\mathrm{1}/\mathrm{2}}…
Question Number 1418 by Rasheed Ahmad last updated on 04/Aug/15 $${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 $$\mathrm{tan}\:\frac{\pi}{\mathrm{4}}=−\mathrm{tan}\:\frac{\mathrm{3}\pi}{\mathrm{4}}=\mathrm{tan}\:\frac{\mathrm{5}\pi}{\mathrm{4}}=−\mathrm{tan}\:\frac{\mathrm{7}\pi}{\mathrm{4}}=\mathrm{1}…
Question Number 1417 by 123456 last updated on 30/Jul/15 $$\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 $${What}\:{to}\:{do}\:{with}\:{it}?\:{Is}\:{it}\:{an}\:{inequation} \\ $$$${to}\:{solve}?\:{Or}\:{is}\:{it}\:{an}\:{identity}\:{to}…
Question Number 132483 by abdullahquwatan last updated on 14/Feb/21 $$\underset{{x}\rightarrow−\mathrm{2}} {\mathrm{lim}}\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}}−{x}^{\mathrm{2}} +\mathrm{2}}{{x}^{\mathrm{5}} +\mathrm{32}}\:\mathrm{no}\:\mathrm{hospital} \\ $$ Commented by EDWIN88 last updated on 14/Feb/21 $$\mathrm{what}\:\mathrm{hospital}? \\…
Question Number 132477 by KZ last updated on 14/Feb/21 $${define} \\ $$$${f}\left({x}.{y}\right)= \\ $$$$\left.\left\{\frac{\mathrm{xy}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \right)\:}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:{if}\:\left({x}.{y}\right)\neq\right)\mathrm{0}.\mathrm{0}\right) \\ $$$$\:\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{if}\:\left({x}.{y}\right)=\left(\mathrm{0}.\mathrm{0}\right) \\ $$$$ \\ $$$${show}\:{that}\:{f},\frac{\partial{f}}{\partial{x}}\:{and}\:\frac{\partial{f}}{\partial{y}\:\:}\:{are}\: \\…
Question Number 1407 by 112358 last updated on 29/Jul/15 $${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}} \\…