Question Number 133469 by Eric002 last updated on 22/Feb/21 $${find}\:{x}\:{in}\:{terms}\:{of}\:{a} \\ $$$$\frac{\mathrm{1}+{x}−\sqrt{\mathrm{2}{x}+{x}^{\mathrm{2}} }}{\mathrm{1}+{x}+\sqrt{\mathrm{2}{x}+{x}^{\mathrm{2}} }}={a}^{\mathrm{3}} \frac{\sqrt{\mathrm{2}+{x}}+\sqrt{{x}}}{\:\sqrt{\mathrm{2}+{x}}−\sqrt{{x}}} \\ $$ Answered by EDWIN88 last updated on 22/Feb/21 $$\frac{\left[\left(\mathrm{1}+\mathrm{x}\right)−\sqrt{\mathrm{2x}+\mathrm{x}^{\mathrm{2}}…
Question Number 133471 by Abdoulaye last updated on 22/Feb/21 $${hos}\:{calcul}\:\int\frac{{lnx}}{{x}^{\mathrm{2}_{} } +\mathrm{1}}{dx}\:? \\ $$ Commented by Dwaipayan Shikari last updated on 22/Feb/21 $${For}\:{General}\:\int_{\mathrm{0}} ^{\infty} \frac{{log}\left({x}\right)}{{x}^{{n}}…
Question Number 67932 by mathmax by abdo last updated on 02/Sep/19 $${let}\:{A}\left(\theta\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)\left({x}^{\mathrm{4}} −{e}^{{i}\theta} \right)}\:\:{with}\:\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}\left(\theta\right)\:{interms}\:{of}\:\theta \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{also}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)\left({x}^{\mathrm{4}} −{e}^{{i}\theta}…
Question Number 133470 by rs4089 last updated on 22/Feb/21 Answered by mr W last updated on 22/Feb/21 $${x}={a}\:\mathrm{cos}\:\theta \\ $$$${y}={b}\:\mathrm{sin}\:\theta \\ $$$${dV}=−\mathrm{2}\pi\left(\mathrm{2}{a}−{a}\:\mathrm{cos}\:\theta\right)\mathrm{2}{ydx} \\ $$$$=\mathrm{4}\pi{a}\left(\mathrm{2}−\mathrm{cos}\:\theta\right){b}\mathrm{sin}\:\theta{a}\mathrm{sin}\:\theta{d}\theta \\…
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Question Number 67931 by mathmax by abdo last updated on 02/Sep/19 $${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:{x}^{{n}} \left\{\mathrm{1}+{cosx}\:+{cos}\left(\mathrm{2}{x}\right)\right\}^{\mathrm{2}} {dx} \\ $$$${find}\:{a}\:{relation}\:{of}\:{recurrence}\:{betwedn}\:{the}\:{A}_{{n}} \\ $$ Terms of Service Privacy…
Question Number 2393 by 123456 last updated on 19/Nov/15 $${f}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R} \\ $$$${x}={a}_{\mathrm{0}} ,{a}_{\mathrm{1}} {a}_{\mathrm{2}} {a}_{\mathrm{3}} … \\ $$$${f}\left({x}\right)=\underset{{i}=\mathrm{0}} {\overset{+\infty} {\sum}}{a}_{{i}} \\ $$$$\mathrm{is}\:{f}\left({x}\right)\:\mathrm{continuous}\:\mathrm{in}\:\mathrm{all}\:{x}\in\left[\mathrm{0},\mathrm{1}\right] \\ $$$${f}\left(\mathrm{0},\mathrm{9999}…\right)=?? \\…
Question Number 67927 by Rasheed.Sindhi last updated on 02/Sep/19 $$\mathrm{Tinku}\:\mathrm{Tara},\mathrm{the}\:\mathrm{developer}. \\ $$$$\mathrm{Sir}, \\ $$$$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{receive}\:\mathrm{notifications}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{forum}.\mathrm{Pl}\:\mathrm{fix}\:\mathrm{the}\:\mathrm{problem}. \\ $$ Commented by TawaTawa last updated on 02/Sep/19…
Question Number 133462 by benjo_mathlover last updated on 22/Feb/21 Answered by TheSupreme last updated on 22/Feb/21 $${both}\:{converge} \\ $$ Commented by benjo_mathlover last updated on…
Question Number 2387 by prakash jain last updated on 18/Nov/15 $$\mathrm{How}\:\mathrm{many}\:\mathrm{0}{s}\:\mathrm{at}\:\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{1000}!? \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{first}\:\mathrm{non}\:\mathrm{zero}\:\mathrm{digits}\:\mathrm{from}\:\mathrm{the}\:\mathrm{right}? \\ $$ Commented by prakash jain last updated on 18/Nov/15 $$\mathrm{Number}\:\mathrm{of}\:\mathrm{zero}\:\mathrm{can}\:\mathrm{be}\:\mathrm{computed}\:\mathrm{using} \\…