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Question Number 164675 Answers: 0 Comments: 5

Question Number 164674 Answers: 0 Comments: 0

Question Number 164672 Answers: 1 Comments: 0

Question Number 164671 Answers: 1 Comments: 1

solve cos^( 3) (x) + sin^( 2) (x) = (7/8) adopted from youtube ...

$$ \\ $$$$\:\:\:\:\:\:\:\:{solve}\: \\ $$$$\:\:\:\:\:\:{cos}^{\:\mathrm{3}} \left({x}\right)\:+\:{sin}^{\:\mathrm{2}} \left({x}\right)\:=\:\frac{\mathrm{7}}{\mathrm{8}}\: \\ $$$$\:\:\:\:\:\:\:\:\:{adopted}\:{from}\:{youtube}\:... \\ $$$$ \\ $$

Question Number 164669 Answers: 0 Comments: 0

Question Number 164650 Answers: 1 Comments: 0

((x+9))^(1/3) −((x−9))^(1/3) = 3 x=?

$$\:\:\sqrt[{\mathrm{3}}]{{x}+\mathrm{9}}\:−\sqrt[{\mathrm{3}}]{{x}−\mathrm{9}}\:=\:\mathrm{3}\: \\ $$$$\:{x}=? \\ $$

Question Number 164653 Answers: 2 Comments: 0

solve 𝛗 = ∫_0 ^( 1) ((ln^( 2) ( x ). tanh^( −1) ( x ))/x)dx =? Ω= ∫_0 ^( 1) (( (tanh^(−1) (x))^( 2) )/(1+x)) = ? −−−−

$$ \\ $$$$\:\:\:\:\:\:\:\:{solve} \\ $$$$\:\:\boldsymbol{\phi}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{ln}^{\:\mathrm{2}} \left(\:{x}\:\right).\:{tanh}^{\:−\mathrm{1}} \left(\:{x}\:\:\right)}{{x}}{dx}\:=? \\ $$$$\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\left({tanh}^{−\mathrm{1}} \left({x}\right)\right)^{\:\mathrm{2}} }{\mathrm{1}+{x}}\:=\:? \\ $$$$\:\:\:\:\:\:−−−− \\ $$

Question Number 164639 Answers: 1 Comments: 0

Question Number 164628 Answers: 1 Comments: 1

60!=abc…nm000…0 m=? n=?

$$\mathrm{60}!=\underline{\boldsymbol{\mathrm{abc}}\ldots\boldsymbol{\mathrm{nm}}\mathrm{000}\ldots\mathrm{0}} \\ $$$$\boldsymbol{\mathrm{m}}=?\:\:\boldsymbol{\mathrm{n}}=? \\ $$

Question Number 164627 Answers: 1 Comments: 0

Question Number 164626 Answers: 1 Comments: 1

Question Number 164623 Answers: 1 Comments: 0

Given a, b ∈ R. Show that : [a]+[b]≤[a+b]≤[a]+[b]+1

$${Given}\:{a},\:{b}\:\in\:\mathbb{R}. \\ $$$${Show}\:{that}\:: \\ $$$$\left[{a}\right]+\left[{b}\right]\leqslant\left[{a}+{b}\right]\leqslant\left[{a}\right]+\left[{b}\right]+\mathrm{1} \\ $$

Question Number 164622 Answers: 2 Comments: 0

Show that ∀ a, b ∈ R, 1. ∣∣x∣−∣y∣∣≤∣x−y∣ 2. 1+∣xy−1∣≤(1+∣x−1∣)(1+∣y−1∣).

$${Show}\:{that}\:\forall\:{a},\:{b}\:\in\:\mathbb{R}, \\ $$$$\mathrm{1}.\:\mid\mid{x}\mid−\mid{y}\mid\mid\leqslant\mid{x}−{y}\mid \\ $$$$\mathrm{2}.\:\mathrm{1}+\mid{xy}−\mathrm{1}\mid\leqslant\left(\mathrm{1}+\mid{x}−\mathrm{1}\mid\right)\left(\mathrm{1}+\mid{y}−\mathrm{1}\mid\right). \\ $$

Question Number 164615 Answers: 0 Comments: 0

Question Number 164612 Answers: 3 Comments: 0

solve: 1. ∫(1/(sinx))dx 2.∫(1/(cosx))dx

$${solve}: \\ $$$$\:\mathrm{1}.\:\int\frac{\mathrm{1}}{{sinx}}{dx} \\ $$$$\:\mathrm{2}.\int\frac{\mathrm{1}}{{cosx}}{dx} \\ $$

Question Number 164609 Answers: 1 Comments: 0

en posant x=t−(1/t) ∫^(+oo) _0 ((1+t^2 )/(1+t^4 ))dt

$${en}\:{posant}\:{x}={t}−\frac{\mathrm{1}}{{t}} \\ $$$$\underset{\mathrm{0}} {\int}^{+{oo}} \frac{\mathrm{1}+{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{4}} }{dt} \\ $$

Question Number 164606 Answers: 2 Comments: 0

Min f(x)= cos 2x +(√3) sin 2x −2(√3) cos x−2sin x is ...

$$\:{Min}\:{f}\left({x}\right)=\:\mathrm{cos}\:\mathrm{2}{x}\:+\sqrt{\mathrm{3}}\:\mathrm{sin}\:\mathrm{2}{x}\:−\mathrm{2}\sqrt{\mathrm{3}}\:\mathrm{cos}\:{x}−\mathrm{2sin}\:{x} \\ $$$$\:{is}\:... \\ $$

Question Number 164605 Answers: 1 Comments: 0

Question Number 164600 Answers: 3 Comments: 0

Question Number 164599 Answers: 0 Comments: 1

180<θ<270 and 2sinθ−cos θ=0 faind volue of sin θ×cos θ=?

$$\mathrm{180}<\theta<\mathrm{270}\:\:\:\:{and} \\ $$$$\mathrm{2}{sin}\theta−\mathrm{cos}\:\theta=\mathrm{0} \\ $$$${faind}\:\:\:{volue}\:{of} \\ $$$$\mathrm{sin}\:\theta×\mathrm{cos}\:\theta=? \\ $$

Question Number 164598 Answers: 0 Comments: 0

Prove that; ∫_(−∞) ^∞ y tan x + y^3 tan x dx = undefined

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}}; \\ $$$$\:\:\:\:\:\:\int_{−\infty} ^{\infty} \:\boldsymbol{{y}}\:\boldsymbol{{tan}}\:\boldsymbol{{x}}\:+\:\boldsymbol{{y}}^{\mathrm{3}} \:\:\boldsymbol{{tan}}\:\:\boldsymbol{{x}}\:\boldsymbol{{dx}}\:=\:\boldsymbol{{undefined}} \\ $$

Question Number 164591 Answers: 1 Comments: 0

pour quelle valeur α la serie converge Σ_(n=2) (ln(n)+αln(n−(1/n))

$${pour}\:{quelle}\:{valeur}\:\alpha\:{la}\:{serie}\:{converge} \\ $$$$\underset{{n}=\mathrm{2}} {\sum}\left({ln}\left({n}\right)+\alpha{ln}\left({n}−\frac{\mathrm{1}}{{n}}\right)\right. \\ $$

Question Number 164590 Answers: 1 Comments: 0

∫ ((In(x^2 .e^(cos2) ))/x) dx

$$\int\:\frac{\mathrm{In}\left(\mathrm{x}^{\mathrm{2}} .\boldsymbol{{e}}^{\boldsymbol{{cos}}\mathrm{2}} \right)}{\boldsymbol{\mathrm{x}}}\:\boldsymbol{\mathrm{dx}} \\ $$

Question Number 164589 Answers: 0 Comments: 0

∫ A.^5 (√(x^3 )) dx

$$\int\:\mathrm{A}.\:^{\mathrm{5}} \sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{3}} \:\:}\:\boldsymbol{\mathrm{dx}} \\ $$

Question Number 164588 Answers: 0 Comments: 0

soit K un corps; pour toute permutation σ de S_n , on note P(σ) sa matrice dans la base canonique de K^n . montrer que deux permutations σ_1 et σ_2 sont conjugues dans S_n si et seulement si P(σ_1 ) et P(σ_2 ) sont semblables.

$${soit}\:{K}\:{un}\:{corps};\:{pour}\:{toute}\:{permutation} \\ $$$$\sigma\:{de}\:{S}_{{n}} ,\:{on}\:{note}\:{P}\left(\sigma\right)\:{sa}\:{matrice}\:{dans}\:{la}\:{base} \\ $$$${canonique}\:{de}\:{K}^{{n}} . \\ $$$${montrer}\:{que}\:{deux}\:{permutations}\:\sigma_{\mathrm{1}} \:{et}\:\sigma_{\mathrm{2}} \:{sont} \\ $$$${conjugues}\:{dans}\:{S}_{{n}} \:{si}\:{et}\:{seulement}\:{si}\: \\ $$$${P}\left(\sigma_{\mathrm{1}} \right)\:{et}\:{P}\left(\sigma_{\mathrm{2}} \right)\:{sont}\:{semblables}. \\ $$

Question Number 164585 Answers: 2 Comments: 0

I = ∫_0 ^( 1) (( Li_( 2) ( x ))/(1 + x)) dx = ? −−−−−−

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\mathcal{I}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\mathrm{Li}_{\:\mathrm{2}} \:\left(\:{x}\:\right)}{\mathrm{1}\:+\:{x}}\:{dx}\:=\:? \\ $$$$\:\:\:\:−−−−−−\: \\ $$

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