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Question Number 149634 Answers: 1 Comments: 0

Trouver toutes les fonctions f:N→R^+ telque ∀(a,b)∈N, f(a^2 +b^2 )=f(a^2 )+f(b^2 ) et f(1)=1

$$\mathrm{Trouver}\:\mathrm{toutes}\:\mathrm{les}\:\mathrm{fonctions}\:\mathrm{f}:\mathbb{N}\rightarrow\mathbb{R}^{+} \\ $$$$\mathrm{telque}\:\forall\left(\mathrm{a},\mathrm{b}\right)\in\mathbb{N}, \\ $$$$\mathrm{f}\left(\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} \right)=\mathrm{f}\left(\mathrm{a}^{\mathrm{2}} \right)+\mathrm{f}\left(\mathrm{b}^{\mathrm{2}} \right)\:\mathrm{et}\:\mathrm{f}\left(\mathrm{1}\right)=\mathrm{1} \\ $$

Question Number 152856 Answers: 0 Comments: 2

Monsieur Puissant, je quitte ce forum mathe^ matique de^ finitivement mais sans avoir dit que j′ai adore^ e^ changer avec vous. Bonne continuation et vive les maths !

$$\mathrm{Monsieur}\:\mathrm{Puissant},\:\mathrm{je}\:\mathrm{quitte}\:\mathrm{ce}\:\mathrm{forum} \\ $$$$\mathrm{math}\acute {\mathrm{e}matique}\:\mathrm{d}\acute {\mathrm{e}finitivement}\:\mathrm{mais} \\ $$$$\mathrm{sans}\:\mathrm{avoir}\:\mathrm{dit}\:\mathrm{que}\:\mathrm{j}'\mathrm{ai}\:\mathrm{ador}\acute {\mathrm{e}}\:\acute {\mathrm{e}changer} \\ $$$$\mathrm{avec}\:\mathrm{vous}. \\ $$$$ \\ $$$$\mathrm{Bonne}\:\mathrm{continuation}\:\mathrm{et}\:\mathrm{vive}\:\mathrm{les} \\ $$$$\mathrm{maths}\:! \\ $$

Question Number 152601 Answers: 2 Comments: 1

solve.... lim_( n→∞) { Π_(k=1) ^n (1 −(k/n)+(k^( 2) /n^( 2) ) )^( (1/n)) }=? m.n...

$$ \\ $$$$\:\:\:{solve}.... \\ $$$$\:\:{lim}_{\:{n}\rightarrow\infty} \left\{\:\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\mathrm{1}\:−\frac{{k}}{{n}}+\frac{{k}^{\:\mathrm{2}} }{{n}^{\:\mathrm{2}} }\:\right)^{\:\frac{\mathrm{1}}{{n}}} \right\}=? \\ $$$$\:\:{m}.{n}... \\ $$$$ \\ $$

Question Number 149628 Answers: 1 Comments: 0

Question Number 149625 Answers: 1 Comments: 0

1)∫_0 ^(2π) (1/(a+sin(t)))dt , a>0 2)∫_(2π) ^(4π) (1/(2+sin(t)))dt..

$$\left.\mathrm{1}\right)\int_{\mathrm{0}} ^{\mathrm{2}\pi} \frac{\mathrm{1}}{\mathrm{a}+\mathrm{sin}\left(\mathrm{t}\right)}\mathrm{dt}\:,\:\mathrm{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\int_{\mathrm{2}\pi} ^{\mathrm{4}\pi} \frac{\mathrm{1}}{\mathrm{2}+\mathrm{sin}\left(\mathrm{t}\right)}\mathrm{dt}.. \\ $$

Question Number 149623 Answers: 1 Comments: 0

Question Number 149621 Answers: 1 Comments: 0

if 2^x =3^y =7^z =((42))^(1/3) find (1/x)+(1/y)+(1/z)=?

$$\mathrm{if}\:\:\:\mathrm{2}^{\boldsymbol{{x}}} =\mathrm{3}^{\boldsymbol{{y}}} =\mathrm{7}^{\boldsymbol{{z}}} =\sqrt[{\mathrm{3}}]{\mathrm{42}} \\ $$$$\mathrm{find}\:\:\:\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}+\frac{\mathrm{1}}{{z}}=? \\ $$

Question Number 149608 Answers: 4 Comments: 0

.....K=∫(1/(1+sin^2 (x)))dx......

$$.....\mathrm{K}=\int\frac{\mathrm{1}}{\mathrm{1}+\mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right)}\mathrm{dx}...... \\ $$

Question Number 149600 Answers: 1 Comments: 0

Question Number 149599 Answers: 0 Comments: 0

Question Number 149598 Answers: 2 Comments: 0

Suppose that sec x + tan x = ((22)/7) cosec x + cot x = (m/n) (m/n) is in the lowest term . Find m + n .

$${Suppose}\:\:{that}\:\: \\ $$$$\mathrm{sec}\:{x}\:+\:\mathrm{tan}\:{x}\:=\:\frac{\mathrm{22}}{\mathrm{7}} \\ $$$$\mathrm{cosec}\:{x}\:+\:\mathrm{cot}\:{x}\:=\:\frac{{m}}{{n}} \\ $$$$\frac{{m}}{{n}}\:\:{is}\:\:{in}\:\:{the}\:\:{lowest}\:\:{term}\:. \\ $$$${Find}\:\:{m}\:+\:{n}\:. \\ $$

Question Number 149596 Answers: 1 Comments: 0

Without L′Hopital lim_(x→π/7) ((sin x sin 2x sin 3x−((√7)/8))/(x−(π/7))) =?

$$\:\mathrm{Without}\:\mathrm{L}'\mathrm{Hopital} \\ $$$$\:\underset{{x}\rightarrow\pi/\mathrm{7}} {\mathrm{lim}}\frac{\mathrm{sin}\:\mathrm{x}\:\mathrm{sin}\:\mathrm{2x}\:\mathrm{sin}\:\mathrm{3x}−\frac{\sqrt{\mathrm{7}}}{\mathrm{8}}}{\mathrm{x}−\frac{\pi}{\mathrm{7}}}\:=? \\ $$

Question Number 149595 Answers: 2 Comments: 1

Question Number 149588 Answers: 2 Comments: 2

{ ((x + (1/y) = 2)),((y + (1/z) = 2)),((z + (1/x) = 2)) :} ⇒ x;y;z=?

$$\begin{cases}{{x}\:+\:\frac{\mathrm{1}}{{y}}\:=\:\mathrm{2}}\\{{y}\:+\:\frac{\mathrm{1}}{{z}}\:=\:\mathrm{2}}\\{{z}\:+\:\frac{\mathrm{1}}{{x}}\:=\:\mathrm{2}}\end{cases}\:\:\:\Rightarrow\:\:{x};{y};{z}=? \\ $$

Question Number 149700 Answers: 2 Comments: 1

Question Number 149585 Answers: 1 Comments: 0

if x;y;z>0 and x^2 +y^2 +z^2 =3 then: Σ ((x^2 +y^2 )/((2x^2 +y^2 )(y^2 +2x^2 ))) ≥ (2/3)

$${if}\:\:{x};{y};{z}>\mathrm{0}\:\:{and}\:\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\mathrm{3}\:\:{then}: \\ $$$$\Sigma\:\frac{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{\left(\mathrm{2}{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)\left({y}^{\mathrm{2}} +\mathrm{2}{x}^{\mathrm{2}} \right)}\:\geqslant\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$

Question Number 149569 Answers: 1 Comments: 0

lim_(x→∞) (((5x + 6)/(2x - 9)))^x^2 = ?

$$\underset{\boldsymbol{\mathrm{x}}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{5x}\:+\:\mathrm{6}}{\mathrm{2x}\:-\:\mathrm{9}}\right)^{\boldsymbol{\mathrm{x}}^{\mathrm{2}} } =\:? \\ $$

Question Number 149568 Answers: 1 Comments: 0

solve the equation: 20z[z] - 21{z} = 2021 where {∗} is GIF and {z} = z - [z]

$${solve}\:{the}\:{equation}: \\ $$$$\mathrm{20}{z}\left[{z}\right]\:-\:\mathrm{21}\left\{{z}\right\}\:=\:\mathrm{2021} \\ $$$${where}\:\left\{\ast\right\}\:{is}\:{GIF}\:\:{and}\:\:\left\{{z}\right\}\:=\:{z}\:-\:\left[{z}\right] \\ $$

Question Number 149567 Answers: 0 Comments: 5

if q is prime number fixed, then solve for natural numbers the equation: (1/q) = (1/x) + (1/y) - (1/z)

$${if}\:\:\boldsymbol{{q}}\:\:{is}\:{prime}\:{number}\:{fixed},\:{then} \\ $$$${solve}\:{for}\:{natural}\:{numbers}\:{the}\:{equation}: \\ $$$$\frac{\mathrm{1}}{{q}}\:=\:\frac{\mathrm{1}}{{x}}\:+\:\frac{\mathrm{1}}{{y}}\:-\:\frac{\mathrm{1}}{{z}} \\ $$

Question Number 152596 Answers: 2 Comments: 0

Question Number 149551 Answers: 1 Comments: 0

Question Number 149547 Answers: 1 Comments: 0

Evaluate lim_(x→(π/7)) ((8cos xcos 2xcos 4x+1)/(x−(π/7)))

$$\:\mathrm{Evaluate}\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{7}}} {\mathrm{lim}}\frac{\mathrm{8cos}\:\mathrm{xcos}\:\mathrm{2xcos}\:\mathrm{4x}+\mathrm{1}}{\mathrm{x}−\frac{\pi}{\mathrm{7}}} \\ $$

Question Number 149534 Answers: 2 Comments: 0

Question Number 149532 Answers: 1 Comments: 0

on realise une suite infinie d′epreuves independantes.chaque epreuve resulte en un succes avec la probabilite p∈]0;1[ ou un echec avec la probabilite q=1−p.soit A_n l′evement “obenir au moins un succes au cours des premieres epreuves.” determiner P(A_n )

$${on}\:{realise}\:{une}\:{suite}\:{infinie}\:{d}'{epreuves} \\ $$$${independantes}.{chaque}\:{epreuve}\:{resulte}\:{en} \\ $$$$\left.{un}\:{succes}\:{avec}\:{la}\:{probabilite}\:{p}\in\right]\mathrm{0};\mathrm{1}\left[\:{ou}\:{un}\right. \\ $$$${echec}\:{avec}\:{la}\:{probabilite}\:{q}=\mathrm{1}−{p}.{soit}\:{A}_{{n}} \\ $$$${l}'{evement}\:``{obenir}\:{au}\:{moins}\:{un}\:{succes}\:{au} \\ $$$${cours}\:{des}\:{premieres}\:{epreuves}.''\:{determiner} \\ $$$${P}\left({A}_{{n}} \right) \\ $$

Question Number 149527 Answers: 1 Comments: 1

Question Number 149516 Answers: 1 Comments: 0

Ω = ∫_( 0) ^( 3) ((√((x + 2)^2 - 8x))) dx = ?

$$\Omega\:=\:\underset{\:\mathrm{0}} {\overset{\:\mathrm{3}} {\int}}\:\left(\sqrt{\left({x}\:+\:\mathrm{2}\right)^{\mathrm{2}} \:-\:\mathrm{8}{x}}\right)\:{dx}\:=\:? \\ $$

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