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Question Number 192160 Answers: 1 Comments: 3

if x,y,z are three distinct complex numbers such that (x/(y−z))+(y/(z−x))+(z/(x−y)) = 0 then find the value of Σ (x^2 /((y−z)^2 ))

$$\mathrm{if}\:\mathrm{x},\mathrm{y},\mathrm{z}\:\mathrm{are}\:\mathrm{three}\:\mathrm{distinct}\:\mathrm{complex}\:\mathrm{numbers} \\ $$$$\mathrm{such}\:\mathrm{that}\:\frac{\mathrm{x}}{\mathrm{y}−{z}}+\frac{\mathrm{y}}{\mathrm{z}−\mathrm{x}}+\frac{\mathrm{z}}{\mathrm{x}−\mathrm{y}}\:=\:\mathrm{0}\:\mathrm{then}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\Sigma\:\frac{\mathrm{x}^{\mathrm{2}} }{\left(\mathrm{y}−\mathrm{z}\right)^{\mathrm{2}} } \\ $$

Question Number 192149 Answers: 5 Comments: 0

Find: (1/2) + (3/2^3 ) + (5/2^5 ) + (7/2^7 ) + ...

$$\mathrm{Find}: \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\mathrm{3}}{\mathrm{2}^{\mathrm{3}} }\:+\:\frac{\mathrm{5}}{\mathrm{2}^{\mathrm{5}} }\:+\:\frac{\mathrm{7}}{\mathrm{2}^{\mathrm{7}} }\:+\:... \\ $$

Question Number 192143 Answers: 1 Comments: 2

Find: (7/2) + ((77)/(22)) + ((777)/(222)) + ((7777)/(2222)) +...+ ((77777777)/(22222222))

$$\mathrm{Find}: \\ $$$$\frac{\mathrm{7}}{\mathrm{2}}\:+\:\frac{\mathrm{77}}{\mathrm{22}}\:+\:\frac{\mathrm{777}}{\mathrm{222}}\:+\:\frac{\mathrm{7777}}{\mathrm{2222}}\:+...+\:\frac{\mathrm{77777777}}{\mathrm{22222222}} \\ $$

Question Number 192142 Answers: 1 Comments: 0

Question let x=<a_n a_(n−1) ...a_1 a_0 > ∈N ; a_0 ≠0 & y=<a_n a_(n−1) ...a_1 > ∈N be two natural numbers such that (x/y)∈N find the number “ x ” ?

$${Question} \\ $$$${let}\:\:\:{x}=<{a}_{{n}} {a}_{{n}−\mathrm{1}} ...{a}_{\mathrm{1}} {a}_{\mathrm{0}} >\:\in\mathbb{N}\:;\:{a}_{\mathrm{0}} \neq\mathrm{0}\:\:\&\: \\ $$$$\:{y}=<{a}_{{n}} {a}_{{n}−\mathrm{1}} ...{a}_{\mathrm{1}} >\:\in\mathbb{N}\:\:{be}\: \\ $$$${two}\:{natural}\:{numbers}\: \\ $$$${such}\:{that}\:\:\frac{{x}}{{y}}\in\mathbb{N}\: \\ $$$${find}\:{the}\:{number}\:``\:{x}\:''\:? \\ $$$$ \\ $$

Question Number 192138 Answers: 1 Comments: 0

show that f(x,y) = {_(0 (x,y)=(0,0)) ^(((x^2 y)/(x^6 + 2y^2 )) (x,y)≠ (0,0)) has a directional derivative in the direction of an arbitrary unit vector φ at (0,0), but f is not continous at (0,0)

$$\mathrm{show}\:\mathrm{that}\: \\ $$$$\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)\:=\:\left\{_{\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{x},\mathrm{y}\right)=\left(\mathrm{0},\mathrm{0}\right)} ^{\frac{\mathrm{x}^{\mathrm{2}} \mathrm{y}}{\mathrm{x}^{\mathrm{6}} \:+\:\mathrm{2y}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{x},\mathrm{y}\right)\neq\:\left(\mathrm{0},\mathrm{0}\right)} \right. \\ $$$$\mathrm{has}\:\mathrm{a}\:\mathrm{directional}\:\mathrm{derivative}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{direction}\:\mathrm{of}\:\mathrm{an}\:\mathrm{arbitrary}\:\mathrm{unit}\:\mathrm{vector} \\ $$$$\phi\:\mathrm{at}\:\left(\mathrm{0},\mathrm{0}\right),\:\mathrm{but}\:\mathrm{f}\:\:\mathrm{is}\:\mathrm{not}\:\mathrm{continous}\:\mathrm{at}\:\left(\mathrm{0},\mathrm{0}\right)\: \\ $$

Question Number 192134 Answers: 1 Comments: 0

when ((√2)+1)^7 =(√(57125))+(√(57124)) then ((√2)−1)^7 =?

$$\mathrm{when}\:\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)^{\mathrm{7}} =\sqrt{\mathrm{57125}}+\sqrt{\mathrm{57124}} \\ $$$$\mathrm{then}\:\:\:\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{7}} =? \\ $$

Question Number 192132 Answers: 1 Comments: 0

What is the nearest point in f(x) to (5,2) where f(x)=−0.5x^2 +3

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{point}\:\mathrm{in}\:{f}\left({x}\right)\:\mathrm{to}\:\left(\mathrm{5},\mathrm{2}\right) \\ $$$$\mathrm{where}\:{f}\left({x}\right)=−\mathrm{0}.\mathrm{5}{x}^{\mathrm{2}} +\mathrm{3} \\ $$

Question Number 192129 Answers: 2 Comments: 0

prove that ∣a+(√(a^2 −b^2 ))∣ + ∣a − (√(a^2 −b^2 ))∣ = ∣a+b∣ +∣a−b∣ a,b ∈ C

$$\:{prove}\:{that} \\ $$$$\:\mid{a}+\sqrt{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }\mid\:+\:\mid{a}\:−\:\sqrt{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }\mid\:=\:\mid{a}+{b}\mid\:+\mid{a}−{b}\mid \\ $$$${a},{b}\:\in\:\mathbb{C} \\ $$

Question Number 192115 Answers: 1 Comments: 0

Ω = lim_( x→0) ( (( cot^( −1) ((1/x) ))/( x)) )^(1/x^( 2) ) = ?

$$ \\ $$$$\:\Omega\:=\:\mathrm{lim}_{\:{x}\rightarrow\mathrm{0}} \:\left(\:\:\frac{\:\mathrm{cot}^{\:−\mathrm{1}} \:\left(\frac{\mathrm{1}}{{x}}\:\right)}{\:{x}}\:\right)^{\frac{\mathrm{1}}{{x}^{\:\mathrm{2}} }} =\:?\:\:\:\:\:\: \\ $$$$\:\: \\ $$$$ \\ $$

Question Number 192112 Answers: 2 Comments: 2

prove that. 0!=1

$${prove}\:{that}.\:\:\:\:\:\:\:\mathrm{0}!=\mathrm{1} \\ $$

Question Number 192172 Answers: 1 Comments: 0

Q1 ∴ x=<1a_1 a_2 ...a_n >∈N & y=<a_1 a_2 ...a_n 1>∈N if y=3x then , find the smallest value of x Q2 ∴ with the above conditions ,what other values can be placed besides the number “ 1 ”

$${Q}\mathrm{1}\:\therefore\:\:{x}=<\mathrm{1}{a}_{\mathrm{1}} {a}_{\mathrm{2}} ...{a}_{{n}} >\in\mathbb{N}\:\:\&\:\:{y}=<{a}_{\mathrm{1}} {a}_{\mathrm{2}} ...{a}_{{n}} \mathrm{1}>\in\mathbb{N} \\ $$$${if}\:\:{y}=\mathrm{3}{x}\:\:{then}\:\:,\:{find}\:{the}\:{smallest}\: \\ $$$${value}\:{of}\:\:{x} \\ $$$${Q}\mathrm{2}\:\therefore\:{with}\:{the}\:{above}\:{conditions}\:,{what}\:{other}\:{values}\: \\ $$$${can}\:{be}\:{placed}\:\:{besides}\:{the}\:{number}\:``\:\mathrm{1}\:''\: \\ $$

Question Number 192105 Answers: 3 Comments: 0

Question Number 192104 Answers: 1 Comments: 0

Question Number 192103 Answers: 1 Comments: 0

Question Number 192099 Answers: 0 Comments: 1

demontrer l expression suivante

$$\mathrm{demontrer}\:\:\mathrm{l}\:\mathrm{expression}\:\mathrm{suivante} \\ $$

Question Number 192098 Answers: 1 Comments: 0

Question Number 192095 Answers: 0 Comments: 0

Prove a non−empty set S of a group G wrt binary operation ∗ is a sub− group of G. Iff 1) a,b ∈ S ⇒ a∗b∈S 2) a ∈ S ⇒ a^(−1) ∈ S. Hello

$$\mathrm{Prove}\:\mathrm{a}\:\mathrm{non}−\mathrm{empty}\:\mathrm{set}\:\mathrm{S}\:\mathrm{of}\:\mathrm{a}\:\mathrm{group} \\ $$$$\mathrm{G}\:\mathrm{wrt}\:\mathrm{binary}\:\mathrm{operation}\:\ast\:\mathrm{is}\:\mathrm{a}\:\mathrm{sub}− \\ $$$$\mathrm{group}\:\mathrm{of}\:\mathrm{G}.\:\mathrm{Iff}\: \\ $$$$\left.\mathrm{1}\right)\:\mathrm{a},\mathrm{b}\:\in\:\mathrm{S}\:\Rightarrow\:\mathrm{a}\ast\mathrm{b}\in\mathrm{S} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{a}\:\in\:\mathrm{S}\:\Rightarrow\:\mathrm{a}^{−\mathrm{1}} \:\in\:\mathrm{S}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Hello} \\ $$

Question Number 192094 Answers: 0 Comments: 0

Prove that the order of a subgroup S of a finite group G, always divide the order of group G.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{order}\:\mathrm{of}\:\mathrm{a}\:\mathrm{subgroup} \\ $$$$\mathrm{S}\:\mathrm{of}\:\mathrm{a}\:\mathrm{finite}\:\mathrm{group}\:\mathrm{G},\:\mathrm{always}\:\mathrm{divide} \\ $$$$\mathrm{the}\:\mathrm{order}\:\mathrm{of}\:\mathrm{group}\:\mathrm{G}. \\ $$

Question Number 192087 Answers: 0 Comments: 3

Let {H_α } ∈ Ω, be a family of subgroup of a group G, then prove that ∩_(α ∈ Ω) H_α .

$$\mathrm{Let}\:\left\{\mathrm{H}_{\alpha} \right\}\:\in\:\Omega,\:\mathrm{be}\:\mathrm{a}\:\mathrm{family}\:\mathrm{of}\: \\ $$$$\mathrm{subgroup}\:\mathrm{of}\:\mathrm{a}\:\mathrm{group}\:\mathrm{G},\:\mathrm{then}\: \\ $$$$\mathrm{prove}\:\mathrm{that}\:\cap_{\alpha\:\in\:\Omega} \mathrm{H}_{\alpha} . \\ $$$$ \\ $$$$ \\ $$

Question Number 192084 Answers: 4 Comments: 0

f(x)+x∙f(−x)=x^2 +1 f((√2))=?

$${f}\left({x}\right)+{x}\centerdot{f}\left(−{x}\right)={x}^{\mathrm{2}} +\mathrm{1} \\ $$$${f}\left(\sqrt{\mathrm{2}}\right)=? \\ $$

Question Number 192083 Answers: 1 Comments: 0

f(x)=ax^2 +bx+c f(x−1)+f(x)+f(x+1)=x^2 +1 f(2)=?

$${f}\left({x}\right)={ax}^{\mathrm{2}} +{bx}+{c} \\ $$$${f}\left({x}−\mathrm{1}\right)+{f}\left({x}\right)+{f}\left({x}+\mathrm{1}\right)={x}^{\mathrm{2}} +\mathrm{1} \\ $$$${f}\left(\mathrm{2}\right)=? \\ $$

Question Number 192080 Answers: 1 Comments: 0

f^(−1) (((x+1)/x))=x^3 f^(−1) (x)+f(8)=?

$${f}^{−\mathrm{1}} \left(\frac{{x}+\mathrm{1}}{{x}}\right)={x}^{\mathrm{3}} \:\: \\ $$$${f}^{−\mathrm{1}} \left({x}\right)+{f}\left(\mathrm{8}\right)=? \\ $$

Question Number 192077 Answers: 1 Comments: 0

Let H be a non−empty subset of a group G, prove that the follow− ing are equivalent 1) H is a subgroup of G 2) for a,b ∈ H, ab^(−1) ∈ H 3) for a,b ∈ ab ∈ H 4) for a ∈ H, a^(−1) ∈ H Hint: prove 1)→2)→3)→4)→1) Help!!!

$$\mathrm{Let}\:\mathrm{H}\:\mathrm{be}\:\mathrm{a}\:\mathrm{non}−\mathrm{empty}\:\mathrm{subset}\:\mathrm{of} \\ $$$$\mathrm{a}\:\mathrm{group}\:\mathrm{G},\:\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{follow}− \\ $$$$\mathrm{ing}\:\mathrm{are}\:\mathrm{equivalent} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{H}\:\mathrm{is}\:\mathrm{a}\:\mathrm{subgroup}\:\mathrm{of}\:\mathrm{G} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{for}\:\mathrm{a},\mathrm{b}\:\in\:\mathrm{H},\:\mathrm{ab}^{−\mathrm{1}} \:\in\:\mathrm{H} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{for}\:\mathrm{a},\mathrm{b}\:\in\:\mathrm{ab}\:\in\:\mathrm{H} \\ $$$$\left.\mathrm{4}\right)\:\mathrm{for}\:\mathrm{a}\:\in\:\mathrm{H},\:\mathrm{a}^{−\mathrm{1}} \:\in\:\mathrm{H} \\ $$$$ \\ $$$$\left.\mathrm{H}\left.\mathrm{i}\left.\mathrm{n}\left.\mathrm{t}\left.:\:\mathrm{prove}\:\mathrm{1}\right)\rightarrow\mathrm{2}\right)\rightarrow\mathrm{3}\right)\rightarrow\mathrm{4}\right)\rightarrow\mathrm{1}\right) \\ $$$$ \\ $$$$\mathrm{Help}!!! \\ $$

Question Number 192076 Answers: 1 Comments: 0

f(x)=x^2 +6x f^(−1) (x)=?

$${f}\left({x}\right)={x}^{\mathrm{2}} +\mathrm{6}{x}\:\:\:\:{f}^{−\mathrm{1}} \left({x}\right)=? \\ $$

Question Number 192073 Answers: 1 Comments: 0

Reponse a l exercice deja pose

$$\mathrm{Reponse}\:\mathrm{a}\:\:\mathrm{l}\:\mathrm{exercice}\:\mathrm{deja}\:\:\mathrm{pose} \\ $$

Question Number 192062 Answers: 2 Comments: 3

prove it : times_n ; (√(4+(√(4+(√(4+...+(√4))))) )) < 3

$${prove}\:{it}\::\: \\ $$$$\:\:\:{times\_n}\:\:\:;\:\:\:\sqrt{\mathrm{4}+\sqrt{\mathrm{4}+\sqrt{\mathrm{4}+...+\sqrt{\mathrm{4}}}}\:\:}\:<\:\mathrm{3} \\ $$

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