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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

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

Question Number 192057    Answers: 1   Comments: 0

Simplify: (((√a) + (√a^2 ) + (√a^3 ) + (√a^4 ))/(((√a) + 1)∙(a + 1)))

$$\mathrm{Simplify}: \\ $$$$\frac{\sqrt{\mathrm{a}}\:\:+\:\:\sqrt{\mathrm{a}^{\mathrm{2}} }\:\:+\:\:\sqrt{\mathrm{a}^{\mathrm{3}} }\:\:+\:\:\sqrt{\mathrm{a}^{\mathrm{4}} }}{\left(\sqrt{\mathrm{a}}\:\:+\:\:\mathrm{1}\right)\centerdot\left(\mathrm{a}\:\:+\:\:\mathrm{1}\right)} \\ $$

Question Number 192054    Answers: 1   Comments: 0

If Q = ((2−x)/(y−1)) ; −5≤x<−1 , 5≤y<6 Find Q_(max) .

$$\:\:\:\mathrm{If}\:\mathrm{Q}\:=\:\frac{\mathrm{2}−\mathrm{x}}{\mathrm{y}−\mathrm{1}}\:;\:−\mathrm{5}\leqslant\mathrm{x}<−\mathrm{1}\:,\:\mathrm{5}\leqslant\mathrm{y}<\mathrm{6} \\ $$$$\:\:\:\mathrm{Find}\:\mathrm{Q}_{\mathrm{max}} .\: \\ $$

Question Number 192049    Answers: 2   Comments: 0

fog(x)=4x−1 g(x)=x−2 f(x)=?

$${fog}\left({x}\right)=\mathrm{4}{x}−\mathrm{1} \\ $$$${g}\left({x}\right)={x}−\mathrm{2} \\ $$$${f}\left({x}\right)=? \\ $$

Question Number 192048    Answers: 1   Comments: 0

if the combined function is h(x)=(√(3x^2 +1)) then find the tow other functions of its.

$${if}\:{the}\:{combined}\:{function}\:{is}\:{h}\left({x}\right)=\sqrt{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$${then}\:{find}\:{the}\:{tow}\:{other}\:{functions}\:{of}\:{its}. \\ $$

Question Number 192047    Answers: 1   Comments: 0

we have three digit number like XYZ that X+Y+Z=16, if we replace X by Z then it will be changed to ZYX number that ZYX=XYZ−594 find XYZ number.

$${we}\:{have}\:{three}\:{digit}\:{number}\:{like}\:{XYZ} \\ $$$${that}\:{X}+{Y}+{Z}=\mathrm{16},\:{if}\:{we}\:{replace}\:{X}\:{by}\:{Z} \\ $$$${then}\:{it}\:{will}\:{be}\:{changed}\:{to}\:{ZYX}\:{number}\: \\ $$$${that}\:{ZYX}={XYZ}−\mathrm{594} \\ $$$${find}\:{XYZ}\:{number}. \\ $$

Question Number 192033    Answers: 2   Comments: 0

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