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Question Number 83063 Answers: 1 Comments: 3

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^2 −b^2 =ab Explicit f(a,b)=∫_0 ^(π/2) (du/(√(a+bsin^2 u)))

$${let}\:\:{a},{b}\:{two}\:{positive}\:{reals}\:{such}\:{as}\:\:{a}^{\mathrm{2}} −{b}^{\mathrm{2}} ={ab} \\ $$$${Explicit}\:\:\:{f}\left({a},{b}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{du}}{\sqrt{{a}+{bsin}^{\mathrm{2}} {u}}}\: \\ $$

Question Number 83037 Answers: 0 Comments: 3

If m=((1−cosθ)/(sinθ)) , show that (1/m)= ((1+sinθ)/(sinθ))

$$\mathrm{If}\:\mathrm{m}=\frac{\mathrm{1}−\mathrm{cos}\theta}{\mathrm{sin}\theta}\:,\:\:\mathrm{show}\:\mathrm{that}\:\frac{\mathrm{1}}{\mathrm{m}}=\:\frac{\mathrm{1}+\mathrm{sin}\theta}{\mathrm{sin}\theta} \\ $$

Question Number 83036 Answers: 0 Comments: 3

Prove that cos^4 θ−sin^4 θ=cos^2 θ−sin^2 θ

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{cos}^{\mathrm{4}} \theta−\mathrm{sin}^{\mathrm{4}} \theta=\mathrm{cos}^{\mathrm{2}} \theta−\mathrm{sin}^{\mathrm{2}} \theta \\ $$

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

(dy/dx) + y sec x = tan x

$$\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\mathrm{y}\:\mathrm{sec}\:\mathrm{x}\:=\:\mathrm{tan}\:\mathrm{x} \\ $$

Question Number 83026 Answers: 0 Comments: 0

Prove that 123456..201820192020 divided by 13 , the remainder is 5 .

$${Prove}\:\:{that} \\ $$$$\:\:\:\:\:\mathrm{123456}..\mathrm{201820192020}\:\:{divided}\:\:{by}\:\:\mathrm{13}\:\:,\:\:{the} \\ $$$${remainder}\:\:{is}\:\:\mathrm{5}\:. \\ $$

Question Number 83021 Answers: 0 Comments: 0

find the sequence v_n wich verify v_n +v_(n+1) =(((−1)^n )/(√n)) (n≥1) is (v_n ) convergente?

$${find}\:{the}\:{sequence}\:{v}_{{n}} \:{wich}\:{verify}\:{v}_{{n}} +{v}_{{n}+\mathrm{1}} =\frac{\left(−\mathrm{1}\right)^{{n}} }{\sqrt{{n}}}\:\:\left({n}\geqslant\mathrm{1}\right) \\ $$$${is}\:\left({v}_{{n}} \right)\:{convergente}? \\ $$

Question Number 83020 Answers: 0 Comments: 0

find the sequence u_n wich verify u_n +u_(n+1) =((sin(n))/n) ∀n>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→0) ((1−(√(1+x+x^2 ))cos(2x))/x^3 )

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\frac{\mathrm{1}−\sqrt{\mathrm{1}+{x}+{x}^{\mathrm{2}} }{cos}\left(\mathrm{2}{x}\right)}{{x}^{\mathrm{3}} } \\ $$

Question Number 83010 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((ch(cos(2x)))/((x^2 +1)^2 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ch}\left({cos}\left(\mathrm{2}{x}\right)\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 83009 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((cos(chx))/(x^2 +3))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({chx}\right)}{{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$

Question Number 83008 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((ch(cosx))/(x^2 +1))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{ch}\left({cosx}\right)}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx} \\ $$

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

lim_(x→0) ((1−(√(1+x^2 ))cos x)/x^4 )

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} \:}\mathrm{cos}\:\mathrm{x}}{\mathrm{x}^{\mathrm{4}} } \\ $$

Question Number 82985 Answers: 1 Comments: 0

Question Number 82975 Answers: 0 Comments: 7

To the member in forum. please give an opinion on this matter. George , Lucia and 12 of their friends will sit around a round table. Many of their arrangements sit if George and Lucia always flank 5 of their friends?

$$\mathrm{To}\:\mathrm{the}\:\mathrm{member}\:\mathrm{in}\:\mathrm{forum}.\:\mathrm{please}\: \\ $$$$\mathrm{give}\:\mathrm{an}\:\mathrm{opinion}\:\mathrm{on}\:\mathrm{this}\:\mathrm{matter}. \\ $$$$\mathrm{George}\:,\:\mathrm{Lucia}\:\mathrm{and}\:\mathrm{12}\:\mathrm{of}\:\mathrm{their} \\ $$$$\mathrm{friends}\:\mathrm{will}\:\mathrm{sit}\:\mathrm{around}\:\mathrm{a}\:\mathrm{round}\:\mathrm{table}. \\ $$$$\mathrm{Many}\:\mathrm{of}\:\mathrm{their}\:\mathrm{arrangements}\:\mathrm{sit}\: \\ $$$$\mathrm{if}\:\mathrm{George}\:\mathrm{and}\:\mathrm{Lucia}\:\mathrm{always}\:\mathrm{flank} \\ $$$$\mathrm{5}\:\mathrm{of}\:\mathrm{their}\:\mathrm{friends}? \\ $$

Question Number 82974 Answers: 1 Comments: 1

Question Number 82973 Answers: 0 Comments: 0

calculate lim_(n→+∞) ∫_0 ^n (1−(x/n))^n arctan(nx)dx

$${calculate}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\int_{\mathrm{0}} ^{{n}} \left(\mathrm{1}−\frac{{x}}{{n}}\right)^{{n}} {arctan}\left({nx}\right){dx} \\ $$

Question Number 82972 Answers: 0 Comments: 0

calculate ∫_0 ^1 arctan(x)ln(1+x)dx

$${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\left({x}\right){ln}\left(\mathrm{1}+{x}\right){dx} \\ $$

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