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Question Number 165778 Answers: 1 Comments: 0

solve for the values of m,n and l l+m+n=0 l^2 +m^2 −n^2 =0

$$\mathrm{solve}\:\mathrm{for}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{m},\mathrm{n}\:\mathrm{and}\:\mathrm{l} \\ $$$$\mathrm{l}+\mathrm{m}+\mathrm{n}=\mathrm{0} \\ $$$$\mathrm{l}^{\mathrm{2}} +\mathrm{m}^{\mathrm{2}} −\mathrm{n}^{\mathrm{2}} =\mathrm{0} \\ $$

Question Number 165774 Answers: 1 Comments: 0

Question Number 165757 Answers: 1 Comments: 0

Question Number 165756 Answers: 0 Comments: 0

Let M be a compact smooth manifold of dimension d. Prove that there exists some n ∈Z^+ such that M can be regularly embedded in the Euclidean space R^n .

$$\mathrm{Let}\:{M}\:\mathrm{be}\:\mathrm{a}\:\mathrm{compact}\:\mathrm{smooth}\:\mathrm{manifold}\:\mathrm{of}\:\mathrm{dimension}\:{d}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{there}\:\mathrm{exists}\:\mathrm{some}\:{n}\:\in\mathbb{Z}^{+} \:\mathrm{such}\:\mathrm{that}\:{M}\:\mathrm{can}\:\mathrm{be}\:\mathrm{regularly}\:\mathrm{embedded}\:\mathrm{in}\:\mathrm{the}\:\mathrm{Euclidean}\:\mathrm{space}\:\mathbb{R}^{{n}} . \\ $$

Question Number 165777 Answers: 1 Comments: 0

The sum of first the n terms of a series {a_n } is given by S_n =3n^2 +n, find Σ_(k=10) ^(20) a_k . A) 910 B) 913 C) 968 D) 1256

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{first}\:\mathrm{the}\:{n}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{series} \\ $$$$\left\{{a}_{{n}} \right\}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:{S}_{{n}} =\mathrm{3}{n}^{\mathrm{2}} +{n},\:\mathrm{find}\:\underset{{k}=\mathrm{10}} {\overset{\mathrm{20}} {\sum}}{a}_{{k}} \:. \\ $$$$\left.\mathrm{A}\right)\:\mathrm{910} \\ $$$$\left.\mathrm{B}\right)\:\mathrm{913} \\ $$$$\left.\mathrm{C}\right)\:\mathrm{968} \\ $$$$\left.\mathrm{D}\right)\:\mathrm{1256}\: \\ $$

Question Number 165776 Answers: 2 Comments: 0

Solve the equation (√(((√x)+1^ )/( (√x)−1 )))−(√(((√x)−1^ )/( (√x)+1 ))) = 1

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:\:\:\sqrt{\frac{\sqrt{{x}}+\mathrm{1}^{} }{\:\sqrt{{x}}−\mathrm{1}\:}}−\sqrt{\frac{\sqrt{{x}}−\mathrm{1}^{} }{\:\sqrt{{x}}+\mathrm{1}\:}}\:=\:\mathrm{1} \\ $$

Question Number 165746 Answers: 1 Comments: 0

compute the extreme points of: f=e^x sin(x+y)

$${compute}\:{the}\:{extreme}\:{points}\:{of}:\: \\ $$$${f}={e}^{{x}} {sin}\left({x}+{y}\right) \\ $$

Question Number 165744 Answers: 2 Comments: 0

Question Number 165737 Answers: 0 Comments: 0

Let alpha is acute angle and cos alpha=3/5 prove that alpha is not r.π where r is rational number

$$ \\ $$Let alpha is acute angle and cos alpha=3/5 prove that alpha is not r.π where r is rational number

Question Number 165893 Answers: 1 Comments: 1

Question Number 165742 Answers: 0 Comments: 0

prove that Σ_(n=0) ^∞ (((2n)!)/((n!)^2 4^n (2n+1)^4 ))=^? (π/(96))(12𝛇(3)+8ln^3 (2)+2π^2 ln(2)) −−−−−−−−by M.A

$$\boldsymbol{{prove}}\:\boldsymbol{{that}} \\ $$$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{2}\boldsymbol{\mathrm{n}}\right)!}{\left(\boldsymbol{\mathrm{n}}!\right)^{\mathrm{2}} \mathrm{4}^{\boldsymbol{\mathrm{n}}} \left(\mathrm{2}\boldsymbol{\mathrm{n}}+\mathrm{1}\right)^{\mathrm{4}} }\overset{?} {=}\frac{\pi}{\mathrm{96}}\left(\mathrm{12}\boldsymbol{\zeta}\left(\mathrm{3}\right)+\mathrm{8}\boldsymbol{\mathrm{ln}}^{\mathrm{3}} \left(\mathrm{2}\right)+\mathrm{2}\pi^{\mathrm{2}} \boldsymbol{\mathrm{ln}}\left(\mathrm{2}\right)\right) \\ $$$$ \\ $$$$−−−−−−−−\boldsymbol{{by}}\:\boldsymbol{{M}}.\boldsymbol{{A}} \\ $$

Question Number 165741 Answers: 2 Comments: 0

∫_0 ^π (dt/(1−sina.cost))=??? , a∈]0,(π/2)[

$$\left.\int_{\mathrm{0}} ^{\pi} \frac{{dt}}{\mathrm{1}−{sina}.{cost}}=???\:,\:{a}\in\right]\mathrm{0},\frac{\pi}{\mathrm{2}}\left[\right. \\ $$

Question Number 165725 Answers: 1 Comments: 0

Show that : ∀ k ∈ N^(∗ ) , (1/(k+1))≤ln(k+1)−ln(k)≤(1/k)

$${Show}\:{that}\::\:\forall\:{k}\:\in\:\mathbb{N}^{\ast\:} ,\: \\ $$$$\frac{\mathrm{1}}{{k}+\mathrm{1}}\leqslant{ln}\left({k}+\mathrm{1}\right)−{ln}\left({k}\right)\leqslant\frac{\mathrm{1}}{{k}} \\ $$

Question Number 165724 Answers: 2 Comments: 0

(U_n )_(n∈N^∗ ) : U_n =Σ_(k=1) ^n (1/k) Show that ∀ n∈N^(∗ ) , U_(2n) −U_n ≥(1/2) . Deduct that lim_(n→+∞) U_n =+∞

$$\left({U}_{{n}} \right)_{{n}\in\mathbb{N}^{\ast} } \::\:{U}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}}\: \\ $$$${Show}\:{that}\:\forall\:{n}\in\mathbb{N}^{\ast\:} ,\:{U}_{\mathrm{2}{n}} −{U}_{{n}} \geqslant\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$.\:{Deduct}\:{that}\:\underset{{n}\rightarrow+\infty} {{lim}}\:{U}_{{n}} =+\infty \\ $$

Question Number 165722 Answers: 1 Comments: 1

Question Number 165699 Answers: 1 Comments: 1

lim_(x→2) ((x−(√(x+2)))/( (√(4x+1)) −3))=....???

$${li}\underset{{x}\rightarrow\mathrm{2}} {{m}}\frac{{x}−\sqrt{{x}+\mathrm{2}}}{\:\sqrt{\mathrm{4}{x}+\mathrm{1}}\:−\mathrm{3}}=....??? \\ $$

Question Number 165698 Answers: 1 Comments: 0

Question Number 165687 Answers: 2 Comments: 0

If f(x)= ((x^( 2) − 2x −8)/(x^( 2) −7x +12)) then ,find : f^( −1) (x)=?

$$ \\ $$$$\:\:\mathrm{I}{f}\:\:\:\:{f}\left({x}\right)=\:\frac{{x}^{\:\mathrm{2}} −\:\mathrm{2}{x}\:−\mathrm{8}}{{x}^{\:\mathrm{2}} −\mathrm{7}{x}\:+\mathrm{12}} \\ $$$$\:\:\:{then}\:,{find}\::\:\:\:\:\:\:\:\:\:\:\:{f}^{\:−\mathrm{1}} \left({x}\right)=? \\ $$$$ \\ $$

Question Number 165685 Answers: 2 Comments: 0

_0 ∫^2 ∣ x^2 −2x+1 ∣ dx =?

$$\:_{\mathrm{0}} \int^{\mathrm{2}} \mid\:{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}\:\mid\:{dx}\:=?\: \\ $$

Question Number 165713 Answers: 1 Comments: 0

Question Number 165731 Answers: 1 Comments: 2

∫ (√(sinx)) dx

$$\int\:\sqrt{{sinx}}\:{dx} \\ $$

Question Number 165673 Answers: 1 Comments: 0

Question Number 165672 Answers: 0 Comments: 0

Question Number 165670 Answers: 0 Comments: 0

Question Number 165669 Answers: 1 Comments: 1

Question Number 165751 Answers: 1 Comments: 0

x^3 +6x−9=0 ⇒x=?

$$\:\mathrm{x}^{\mathrm{3}} +\mathrm{6x}−\mathrm{9}=\mathrm{0}\:\Rightarrow\mathrm{x}=? \\ $$

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