Question and Answers Forum

AllQuestion and Answers: Page 686

Question Number 149718 Answers: 1 Comments: 0

Question Number 149686 Answers: 2 Comments: 2

Question Number 149675 Answers: 0 Comments: 0

lim_(n→∞) ((∫_( 0) ^( ∞) (dx/((x^2 + (1/4))^(n+1) ))))^(1/n) = ?

$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\sqrt[{\boldsymbol{\mathrm{n}}}]{\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)^{\boldsymbol{\mathrm{n}}+\mathrm{1}} }}\:=\:? \\ $$

Question Number 149673 Answers: 3 Comments: 0

solve :: [ 1] 𝛗 := ∫_0 ^( ∞ ) ((ln^( 2) (e x ))/(e^( 4) +x^( 2) )) dx =((π k)/e^( 2) ) k:= ? [ 2 ] Ω := ∫_(0 ) ^( ∞) (( ln^( 3) (x ))/( e^( 2) + x^( 2) )) dx = ?

$$\:\:\:\mathrm{solve}\::: \\ $$$$\left[\:\mathrm{1}\right]\:\:\:\:\boldsymbol{\phi}\::=\:\int_{\mathrm{0}} ^{\:\:\infty\:} \frac{{ln}^{\:\mathrm{2}} \:\left({e}\:{x}\:\right)}{{e}^{\:\mathrm{4}} \:+{x}^{\:\mathrm{2}} }\:{dx}\:=\frac{\pi\:{k}}{{e}^{\:\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{k}:=\:? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\left[\:\mathrm{2}\:\right]\:\:\:\Omega\::=\:\int_{\mathrm{0}\:} ^{\:\infty} \:\frac{\:{ln}^{\:\mathrm{3}} \:\left({x}\:\right)}{\:{e}^{\:\mathrm{2}} +\:{x}^{\:\mathrm{2}} }\:{dx}\:=\:? \\ $$

Question Number 149670 Answers: 1 Comments: 0

Solve the equation x=(√(a−(√(a+x)) )) where a>0 is a parameter.

$$\:\:\:{Solve}\:{the}\:{equation}\: \\ $$$$\:\:{x}=\sqrt{{a}−\sqrt{{a}+{x}}\:}\:{where}\:{a}>\mathrm{0}\:{is}\: \\ $$$$\:{a}\:{parameter}. \\ $$

Question Number 149667 Answers: 2 Comments: 0

f (x )= (1/( (√( 1 + sin (x ))) +(√( 1 + cos (x))))) find: Min( f (x)) =?

$$\: \\ $$$${f}\:\left({x}\:\right)=\:\frac{\mathrm{1}}{\:\sqrt{\:\mathrm{1}\:+\:{sin}\:\left({x}\:\right)}\:+\sqrt{\:\mathrm{1}\:+\:{cos}\:\left({x}\right)}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{find}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Min}\left(\:{f}\:\left({x}\right)\right)\:=? \\ $$$$ \\ $$

Question Number 149660 Answers: 1 Comments: 0

Question Number 150362 Answers: 1 Comments: 0

Given that p=(3i+4j) , q=(2i−j) and r=5i−j. Express vector r intrems of p and q .

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{p}=\left(\mathrm{3i}+\mathrm{4j}\right)\:,\:\mathrm{q}=\left(\mathrm{2i}−\mathrm{j}\right)\:\mathrm{and} \\ $$$$\mathrm{r}=\mathrm{5i}−\mathrm{j}.\:\mathrm{Express}\:\:\mathrm{vector}\:\:\:\mathrm{r}\:\:\mathrm{intrems}\:\mathrm{of} \\ $$$$\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:. \\ $$

Question Number 149638 Answers: 0 Comments: 0

Question Number 149637 Answers: 2 Comments: 0

Question Number 149636 Answers: 1 Comments: 0

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