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AllQuestion and Answers: Page 587

Question Number 160544 Answers: 0 Comments: 2

Question Number 160543 Answers: 0 Comments: 0

lim_( x→ 6) (( Γ ( sin( (π/x)))−Γ ((3/x) ))/(sin( πx )))= ?

$$ \\ $$$$\mathrm{lim}_{\:{x}\rightarrow\:\mathrm{6}} \frac{\:\Gamma\:\left(\:{sin}\left(\:\frac{\pi}{{x}}\right)\right)−\Gamma\:\left(\frac{\mathrm{3}}{{x}}\:\right)}{{sin}\left(\:\pi{x}\:\right)}=\:? \\ $$$$ \\ $$

Question Number 160539 Answers: 1 Comments: 0

Prove by recurrence that (1/(n!))≤(1/2^(n−1) ), ∀n≥1.

$${Prove}\:{by}\:{recurrence}\:{that} \\ $$$$\frac{\mathrm{1}}{{n}!}\leqslant\frac{\mathrm{1}}{\mathrm{2}^{{n}−\mathrm{1}} },\:\forall{n}\geqslant\mathrm{1}. \\ $$

Question Number 160530 Answers: 2 Comments: 0

Question Number 160529 Answers: 2 Comments: 0

Resolve u_n −3u_(n−1) =12((3/4))^n and u_n =2u_(n−1) +5cos (n(Π/3)), u_o =1

$${Resolve}\: \\ $$$$\:{u}_{{n}} −\mathrm{3}{u}_{{n}−\mathrm{1}} =\mathrm{12}\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{{n}} \:\:{and} \\ $$$$\:{u}_{{n}} =\mathrm{2}{u}_{{n}−\mathrm{1}} +\mathrm{5cos}\:\left({n}\frac{\Pi}{\mathrm{3}}\right),\:\:{u}_{{o}} =\mathrm{1} \\ $$

Question Number 160528 Answers: 0 Comments: 0

(2cosh(x)cos(y))dx+(sinh(x)sin(y))dy=0

$$\left(\mathrm{2}\boldsymbol{\mathrm{cosh}}\left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{y}}\right)\right)\boldsymbol{\mathrm{dx}}+\left(\boldsymbol{\mathrm{sinh}}\left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{sin}}\left(\boldsymbol{\mathrm{y}}\right)\right)\boldsymbol{\mathrm{dy}}=\mathrm{0} \\ $$

Question Number 160526 Answers: 1 Comments: 0

Montre que Sup(A−B)=Sup(A)−Inf(B) Avec A−B={a−b ; a∈ A , b∈ B}

$${Montre}\:{que}\:{Sup}\left({A}−{B}\right)={Sup}\left({A}\right)−{Inf}\left({B}\right) \\ $$$${Avec}\:{A}−{B}=\left\{{a}−{b}\:;\:{a}\in\:{A}\:,\:{b}\in\:{B}\right\} \\ $$

Question Number 160522 Answers: 1 Comments: 0

Question Number 160521 Answers: 0 Comments: 0

(y^2 +4y)(√(x+2))=(2x+1)(y+1) (((2x+1)/y))^2 +x=2y^2 +10y+3

$$\left({y}^{\mathrm{2}} +\mathrm{4}{y}\right)\sqrt{{x}+\mathrm{2}}=\left(\mathrm{2}{x}+\mathrm{1}\right)\left({y}+\mathrm{1}\right) \\ $$$$\left(\frac{\mathrm{2}{x}+\mathrm{1}}{{y}}\right)^{\mathrm{2}} +{x}=\mathrm{2}{y}^{\mathrm{2}} +\mathrm{10}{y}+\mathrm{3} \\ $$

Question Number 160520 Answers: 1 Comments: 0

Given data : 1,3,3,5,5,5,5,8,9,10,10,12 find the value of quartile 1^(st)

$$\:\mathrm{Given}\:\mathrm{data}\::\:\mathrm{1},\mathrm{3},\mathrm{3},\mathrm{5},\mathrm{5},\mathrm{5},\mathrm{5},\mathrm{8},\mathrm{9},\mathrm{10},\mathrm{10},\mathrm{12} \\ $$$$\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{quartile}\:\mathrm{1}^{\mathrm{st}} \\ $$

Question Number 160516 Answers: 1 Comments: 0

Question Number 160508 Answers: 0 Comments: 0

f(x)=27x^3 +5x^2 −2 lim_(x→∞) ((f^(−1) (27x)−f^(−1) (x))/( (x)^(1/3) ))=?

$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{27x}^{\mathrm{3}} +\mathrm{5x}^{\mathrm{2}} −\mathrm{2} \\ $$$$\underset{\mathrm{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{f}^{−\mathrm{1}} \left(\mathrm{27x}\right)−\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)}{\:\sqrt[{\mathrm{3}}]{\mathrm{x}}}=? \\ $$

Question Number 160507 Answers: 0 Comments: 0

Question Number 160506 Answers: 0 Comments: 0

Question Number 160504 Answers: 1 Comments: 2

Question Number 160496 Answers: 2 Comments: 0

Question Number 160493 Answers: 1 Comments: 0

montrer a l aide de binome de newton que: Σ_(k=o) ^r (^n _k )(_(r−k) ^m )=(_( r) ^(m+n) )

$${montrer}\:{a}\:{l}\:{aide}\:{de}\:{binome}\:{de}\:{newton}\:{que}:\: \\ $$$$\underset{{k}={o}} {\overset{{r}} {\sum}}\left(\underset{{k}} {\:}^{{n}} \right)\left(_{{r}−{k}} ^{{m}} \right)=\left(_{\:\:\:\:\:{r}} ^{{m}+{n}} \right)\: \\ $$

Question Number 160491 Answers: 0 Comments: 1

Question Number 160487 Answers: 3 Comments: 0

Question Number 160482 Answers: 2 Comments: 1

Question Number 160473 Answers: 1 Comments: 0

Question Number 160466 Answers: 0 Comments: 0

Question Number 160457 Answers: 2 Comments: 0

Simplfy: ((1 + cos𝛂)/(sin^2 𝛂)) : (1 + (((1 + cos𝛂)/(sin𝛂)))^2 )

$$\mathrm{Simplfy}: \\ $$$$\frac{\mathrm{1}\:+\:\mathrm{cos}\boldsymbol{\alpha}}{\mathrm{sin}^{\mathrm{2}} \boldsymbol{\alpha}}\::\:\left(\mathrm{1}\:+\:\left(\frac{\mathrm{1}\:+\:\mathrm{cos}\boldsymbol{\alpha}}{\mathrm{sin}\boldsymbol{\alpha}}\right)^{\mathrm{2}} \right) \\ $$

Question Number 160451 Answers: 2 Comments: 0

Solve the differential system below: { ((y_1 ′=2y_1 +y_2 +y_3 )),((y_2 ′=−2y_1 −y_3 )),((y_3 ′=2y_1 +y_2 +2y_3 )) :}

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{system}\:\mathrm{below}: \\ $$$$\begin{cases}{{y}_{\mathrm{1}} '=\mathrm{2}{y}_{\mathrm{1}} +{y}_{\mathrm{2}} +{y}_{\mathrm{3}} }\\{{y}_{\mathrm{2}} '=−\mathrm{2}{y}_{\mathrm{1}} −{y}_{\mathrm{3}} }\\{{y}_{\mathrm{3}} '=\mathrm{2}{y}_{\mathrm{1}} +{y}_{\mathrm{2}} +\mathrm{2}{y}_{\mathrm{3}} }\end{cases} \\ $$

Question Number 160445 Answers: 1 Comments: 2

Find: ((√2)/2) ∙ ((√(2 + (√2)))/2) ∙ ((√(2 + (√(2 + (√2)))))/2) ∙ ... = ?

$$\mathrm{Find}: \\ $$$$\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\:\centerdot\:\frac{\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{2}}}}{\mathrm{2}}\:\centerdot\:\frac{\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{2}}}}}{\mathrm{2}}\:\centerdot\:...\:=\:? \\ $$

Question Number 160444 Answers: 2 Comments: 0

Find: lim_(x→2) ((Γ((1/x) + 1) - ((√π)/x))/(x^3 - 8)) = ?

$$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{\Gamma\left(\frac{\mathrm{1}}{\mathrm{x}}\:+\:\mathrm{1}\right)\:-\:\frac{\sqrt{\pi}}{\mathrm{x}}}{\mathrm{x}^{\mathrm{3}} \:-\:\mathrm{8}}\:=\:? \\ $$

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