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Question Number 155310 Answers: 1 Comments: 0

lim U_n =Σ_(k=o) ^(n−1) ((n(ln(n+k))−ln(n))/(n^2 +k^2 ))

$$\mathrm{lim}\:\:\:\:{U}_{{n}} =\underset{{k}={o}} {\overset{{n}−\mathrm{1}} {\sum}}\:\:\frac{{n}\left({ln}\left({n}+{k}\right)\right)−{ln}\left({n}\right)}{{n}^{\mathrm{2}} +{k}^{\mathrm{2}} } \\ $$

Question Number 155302 Answers: 0 Comments: 0

Question Number 155295 Answers: 0 Comments: 2

Evaluate: lim_(n→∞) ((Σ n)/n^2 ) = ?

$$\mathrm{Evaluate}:\:\:\:\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\frac{\Sigma\:\boldsymbol{\mathrm{n}}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }\:=\:? \\ $$

Question Number 155294 Answers: 1 Comments: 0

Question Number 155293 Answers: 2 Comments: 0

Question Number 155292 Answers: 1 Comments: 0

Question Number 155285 Answers: 0 Comments: 0

Question Number 155281 Answers: 1 Comments: 0

f :[ 0 , 6] → [−4 , 4] f (0 )=0 f (6 )=4 x, y≥0 , x+y ≤6 f (x+y )=(1/4){f(x)(√(16−(f(y))^2 )) +f(y)(√(16−(f(x))^2 )) } ∴ ( f(1) +f (3))^( 2) =?

$$ \\ $$$$\:{f}\::\left[\:\mathrm{0}\:,\:\:\mathrm{6}\right]\:\rightarrow\:\left[−\mathrm{4}\:,\:\mathrm{4}\right] \\ $$$$\:\:\:{f}\:\left(\mathrm{0}\:\right)=\mathrm{0} \\ $$$$\:\:\:\:{f}\:\left(\mathrm{6}\:\right)=\mathrm{4}\: \\ $$$$\:\:{x},\:\:{y}\geqslant\mathrm{0}\:\:,\:{x}+{y}\:\leqslant\mathrm{6} \\ $$$$\:\:\:{f}\:\left({x}+{y}\:\right)=\frac{\mathrm{1}}{\mathrm{4}}\left\{{f}\left({x}\right)\sqrt{\mathrm{16}−\left({f}\left({y}\right)\right)^{\mathrm{2}} }\:+{f}\left({y}\right)\sqrt{\mathrm{16}−\left({f}\left({x}\right)\right)^{\mathrm{2}} }\:\right\} \\ $$$$\:\:\therefore\:\:\:\left(\:{f}\left(\mathrm{1}\right)\:+{f}\:\left(\mathrm{3}\right)\right)^{\:\mathrm{2}} =? \\ $$

Question Number 155277 Answers: 2 Comments: 0

Question Number 155272 Answers: 0 Comments: 3

Question Number 155265 Answers: 1 Comments: 0

si E est la fonction partie entiere ,et n un entier naturel alors I=∫_o ^n E(x) vaut?

$${si}\:{E}\:{est}\:{la}\:{fonction}\:{partie}\:{entiere}\:,{et}\:{n}\:{un}\:{entier}\:{naturel} \\ $$$${alors}\:{I}=\int_{{o}} ^{{n}} {E}\left({x}\right)\:{vaut}? \\ $$

Question Number 155252 Answers: 1 Comments: 0

∫_0 ^( (π/2)) x.sin^( 2) (x).ln(sin(x))dx

$$ \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {x}.{sin}^{\:\mathrm{2}} \left({x}\right).{ln}\left({sin}\left({x}\right)\right){dx} \\ $$

Question Number 155244 Answers: 2 Comments: 0

Solve the equation: (sinx)^3 + sinx = cosx

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$ \\ $$$$\left(\mathrm{sin}\boldsymbol{\mathrm{x}}\right)^{\mathrm{3}} \:+\:\mathrm{sin}\boldsymbol{\mathrm{x}}\:=\:\mathrm{cos}\boldsymbol{\mathrm{x}} \\ $$

Question Number 155243 Answers: 0 Comments: 2

the value of the integral ∫_(−1) ^( 1) x^2 p_2 (x) dx is ?

$$\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{integral}}\:\int_{−\mathrm{1}} ^{\:\mathrm{1}} \:\boldsymbol{{x}}^{\mathrm{2}} \:\boldsymbol{{p}}_{\mathrm{2}} \left(\boldsymbol{{x}}\right)\:\boldsymbol{{dx}}\:\:\:\boldsymbol{{is}}\:?\: \\ $$

Question Number 155242 Answers: 1 Comments: 1

the value of 𝛃 (2, n ) is ?

$$\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\:\boldsymbol{\beta}\:\left(\mathrm{2},\:{n}\:\right)\:\boldsymbol{{is}}\:? \\ $$

Question Number 155238 Answers: 0 Comments: 0

Question Number 155236 Answers: 0 Comments: 0

Question Number 155237 Answers: 1 Comments: 0

If Ω = ∫_0 ^( ∞) (( ln^( 2) (x ).sin((√(x )) ))/x) dx prove that : Ω = 4 γ^( 2) + (π^( 3) /3) ■ m.n

$$ \\ $$$$\:\:\mathrm{I}{f}\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{ln}^{\:\mathrm{2}} \left({x}\:\right).{sin}\left(\sqrt{{x}\:}\:\right)}{{x}}\:{dx} \\ $$$$\:\:\:\:\:{prove}\:{that}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega\:=\:\mathrm{4}\:\gamma^{\:\mathrm{2}} \:+\:\frac{\pi^{\:\mathrm{3}} }{\mathrm{3}}\:\:\:\:\:\blacksquare\:{m}.{n} \\ $$

Question Number 155231 Answers: 0 Comments: 0

f (x) :=(√((1/a) +x)) −(√((1/a) −x)) and D_f ≠ ∅ , g(x)=(√((ax−1)/(f^( −1) ( ax −a )))) find : D_( g) =?

$$ \\ $$$$\:\:\:{f}\:\left({x}\right)\::=\sqrt{\frac{\mathrm{1}}{{a}}\:+{x}}\:−\sqrt{\frac{\mathrm{1}}{{a}}\:−{x}} \\ $$$$\:\:{and}\:\:\:\:\mathrm{D}_{{f}} \:\neq\:\varnothing\:, \\ $$$$\:\:\:\:\:\:\:{g}\left({x}\right)=\sqrt{\frac{{ax}−\mathrm{1}}{{f}^{\:−\mathrm{1}} \left(\:{ax}\:−{a}\:\right)}} \\ $$$$\:\:\:\:\:\:\:\:{find}\::\:\:\mathrm{D}_{\:{g}} \:=? \\ $$

Question Number 155225 Answers: 0 Comments: 3

Question Number 155217 Answers: 0 Comments: 0

∫_(−∞) ^( ∞) ((ln((√(x^4 +1))))/( (√(x^4 +1)))) dx

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{−\infty} ^{\:\infty} \:\frac{\mathrm{ln}\left(\sqrt{{x}^{\mathrm{4}} +\mathrm{1}}\right)}{\:\sqrt{{x}^{\mathrm{4}} +\mathrm{1}}}\:\:{dx} \\ $$$$\: \\ $$

Question Number 155215 Answers: 2 Comments: 0

Question Number 155212 Answers: 0 Comments: 1

Question Number 155204 Answers: 3 Comments: 0

Solve for positive integers: abcd + abc = (a+1)(b+1)(c+1)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{positive}\:\mathrm{integers}: \\ $$$$\mathrm{abcd}\:+\:\mathrm{abc}\:=\:\left(\mathrm{a}+\mathrm{1}\right)\left(\mathrm{b}+\mathrm{1}\right)\left(\mathrm{c}+\mathrm{1}\right) \\ $$

Question Number 155203 Answers: 1 Comments: 0

Question Number 155196 Answers: 1 Comments: 2

Hi I forgot my password, is there a way I can get it ?

$${Hi}\:{I}\:{forgot}\:{my}\:{password},\: \\ $$$${is}\:{there}\:{a}\:{way}\:{I}\:{can}\:{get}\:{it}\:? \\ $$

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