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Question Number 83050 Answers: 0 Comments: 1
Question Number 83049 Answers: 0 Comments: 0
Question Number 83042 Answers: 0 Comments: 1
$${let}\:\:{a},{b}\:{two}\:{positive}\:{reals}\:{such}\:{as}\:\:{a}^{\mathrm{2}} −{b}^{\mathrm{2}} ={ab} \\ $$$${Explicit}\:\:\:{f}\left({a},{b}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{du}}{\sqrt{{a}+{bsin}^{\mathrm{2}} {u}}}\: \\ $$
Question Number 83037 Answers: 0 Comments: 3
$$\mathrm{If}\:\mathrm{m}=\frac{\mathrm{1}−\mathrm{cos}\theta}{\mathrm{sin}\theta}\:,\:\:\mathrm{show}\:\mathrm{that}\:\frac{\mathrm{1}}{\mathrm{m}}=\:\frac{\mathrm{1}+\mathrm{sin}\theta}{\mathrm{sin}\theta} \\ $$
Question Number 83036 Answers: 0 Comments: 3
$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{cos}^{\mathrm{4}} \theta−\mathrm{sin}^{\mathrm{4}} \theta=\mathrm{cos}^{\mathrm{2}} \theta−\mathrm{sin}^{\mathrm{2}} \theta \\ $$
Question Number 83035 Answers: 1 Comments: 1
Question Number 83032 Answers: 1 Comments: 0
Question Number 83030 Answers: 1 Comments: 0
Question Number 83028 Answers: 0 Comments: 3
$$\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\mathrm{y}\:\mathrm{sec}\:\mathrm{x}\:=\:\mathrm{tan}\:\mathrm{x} \\ $$
Question Number 83026 Answers: 0 Comments: 0
$${Prove}\:\:{that} \\ $$$$\:\:\:\:\:\mathrm{123456}..\mathrm{201820192020}\:\:{divided}\:\:{by}\:\:\mathrm{13}\:\:,\:\:{the} \\ $$$${remainder}\:\:{is}\:\:\mathrm{5}\:. \\ $$
Question Number 83021 Answers: 0 Comments: 0
$${find}\:{the}\:{sequence}\:{v}_{{n}} \:{wich}\:{verify}\:{v}_{{n}} +{v}_{{n}+\mathrm{1}} =\frac{\left(−\mathrm{1}\right)^{{n}} }{\sqrt{{n}}}\:\:\left({n}\geqslant\mathrm{1}\right) \\ $$$${is}\:\left({v}_{{n}} \right)\:{convergente}? \\ $$
Question Number 83020 Answers: 0 Comments: 0
$${find}\:{the}\:{sequence}\:{u}_{{n}} \:{wich}\:{verify}\:{u}_{{n}} +{u}_{{n}+\mathrm{1}} =\frac{{sin}\left({n}\right)}{{n}}\:\:\forall{n}>\mathrm{0} \\ $$
Question Number 83019 Answers: 1 Comments: 1
$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\frac{\mathrm{1}−\sqrt{\mathrm{1}+{x}+{x}^{\mathrm{2}} }{cos}\left(\mathrm{2}{x}\right)}{{x}^{\mathrm{3}} } \\ $$
Question Number 83010 Answers: 0 Comments: 0
$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ch}\left({cos}\left(\mathrm{2}{x}\right)\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$
Question Number 83009 Answers: 0 Comments: 1
$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({chx}\right)}{{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$
Question Number 83008 Answers: 0 Comments: 0
$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{ch}\left({cosx}\right)}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx} \\ $$
Question Number 82995 Answers: 1 Comments: 1
Question Number 82993 Answers: 1 Comments: 0
Question Number 82991 Answers: 1 Comments: 2
Question Number 82988 Answers: 1 Comments: 3
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} \:}\mathrm{cos}\:\mathrm{x}}{\mathrm{x}^{\mathrm{4}} } \\ $$
Question Number 82985 Answers: 1 Comments: 0
Question Number 82975 Answers: 0 Comments: 7
$$\mathrm{To}\:\mathrm{the}\:\mathrm{member}\:\mathrm{in}\:\mathrm{forum}.\:\mathrm{please}\: \\ $$$$\mathrm{give}\:\mathrm{an}\:\mathrm{opinion}\:\mathrm{on}\:\mathrm{this}\:\mathrm{matter}. \\ $$$$\mathrm{George}\:,\:\mathrm{Lucia}\:\mathrm{and}\:\mathrm{12}\:\mathrm{of}\:\mathrm{their} \\ $$$$\mathrm{friends}\:\mathrm{will}\:\mathrm{sit}\:\mathrm{around}\:\mathrm{a}\:\mathrm{round}\:\mathrm{table}. \\ $$$$\mathrm{Many}\:\mathrm{of}\:\mathrm{their}\:\mathrm{arrangements}\:\mathrm{sit}\: \\ $$$$\mathrm{if}\:\mathrm{George}\:\mathrm{and}\:\mathrm{Lucia}\:\mathrm{always}\:\mathrm{flank} \\ $$$$\mathrm{5}\:\mathrm{of}\:\mathrm{their}\:\mathrm{friends}? \\ $$
Question Number 82974 Answers: 1 Comments: 1
Question Number 82973 Answers: 0 Comments: 0
$${calculate}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\int_{\mathrm{0}} ^{{n}} \left(\mathrm{1}−\frac{{x}}{{n}}\right)^{{n}} {arctan}\left({nx}\right){dx} \\ $$
Question Number 82972 Answers: 0 Comments: 0
$${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\left({x}\right){ln}\left(\mathrm{1}+{x}\right){dx} \\ $$
Question Number 82971 Answers: 1 Comments: 2
$$\left.\mathrm{1}\right){find}\:\int\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{6}} } \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{−\infty} ^{+\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{6}} } \\ $$
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