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Question Number 163467 Answers: 1 Comments: 0

Question Number 163463 Answers: 1 Comments: 0

nature de la serie Σ_(n=1) ((1/(n+1))+(1/n))

$${nature}\:{de}\:{la}\:{serie} \\ $$$$\underset{{n}=\mathrm{1}} {\sum}\left(\frac{\mathrm{1}}{{n}+\mathrm{1}}+\frac{\mathrm{1}}{{n}}\right) \\ $$

Question Number 163457 Answers: 0 Comments: 1

let a>0 and 𝛌>0 fixed solve for (0;∞) the equation: 2a^2 cos((x/(2λ)) - ((2λ)/x)) = a^(x/𝛌) + a^((4𝛌)/x)

$$\mathrm{let}\:\:\boldsymbol{\mathrm{a}}>\mathrm{0}\:\:\mathrm{and}\:\:\boldsymbol{\lambda}>\mathrm{0}\:\:\mathrm{fixed} \\ $$$$\mathrm{solve}\:\mathrm{for}\:\:\left(\mathrm{0};\infty\right)\:\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\mathrm{2a}^{\mathrm{2}} \mathrm{cos}\left(\frac{\mathrm{x}}{\mathrm{2}\lambda}\:-\:\frac{\mathrm{2}\lambda}{\mathrm{x}}\right)\:=\:\mathrm{a}^{\frac{\boldsymbol{\mathrm{x}}}{\boldsymbol{\lambda}}} \:\:+\:\:\mathrm{a}^{\frac{\mathrm{4}\boldsymbol{\lambda}}{\boldsymbol{\mathrm{x}}}} \\ $$

Question Number 163452 Answers: 1 Comments: 1

Solve for real numbers: 3^(x (√x)) + 3^(1 + (1/( (√x)))) = 12

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{3}^{\boldsymbol{\mathrm{x}}\:\sqrt{\boldsymbol{\mathrm{x}}}} \:\:+\:\:\mathrm{3}^{\mathrm{1}\:+\:\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{\mathrm{x}}}}} \:\:=\:\mathrm{12} \\ $$

Question Number 163451 Answers: 0 Comments: 1

Solve for real numbers: (√(1 - x)) = 1 - 2x^2 + 2x (√(1 - x^2 ))

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\sqrt{\mathrm{1}\:-\:\mathrm{x}}\:=\:\mathrm{1}\:-\:\mathrm{2x}^{\mathrm{2}} \:+\:\mathrm{2x}\:\sqrt{\mathrm{1}\:-\:\mathrm{x}^{\mathrm{2}} } \\ $$

Question Number 163443 Answers: 0 Comments: 7

p ≤ n find (A_n ^p /A_(n−1) ^p ).

$$\mathrm{p}\:\leqslant\:\mathrm{n}\: \\ $$$$\mathrm{find}\:\:\frac{\mathrm{A}_{\mathrm{n}} ^{\mathrm{p}} }{\mathrm{A}_{\mathrm{n}−\mathrm{1}} ^{\mathrm{p}} }. \\ $$

Question Number 163441 Answers: 0 Comments: 0

∫((x+3)/((x+1)^4 ))dx=∫((x+1+3)/((x+1)^4 ))dx=∫(1/((x+1)^3 ))dx+3∫(1/((x+1)^4 ))dx

$$\int\frac{{x}+\mathrm{3}}{\left({x}+\mathrm{1}\right)^{\mathrm{4}} }{dx}=\int\frac{{x}+\mathrm{1}+\mathrm{3}}{\left({x}+\mathrm{1}\right)^{\mathrm{4}} }{dx}=\int\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} }{dx}+\mathrm{3}\int\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{4}} }{dx} \\ $$

Question Number 163439 Answers: 0 Comments: 0

Question Number 163437 Answers: 1 Comments: 2

Question Number 163434 Answers: 0 Comments: 0

Question Number 163433 Answers: 0 Comments: 0

Question Number 163432 Answers: 1 Comments: 0

Question Number 163430 Answers: 1 Comments: 0

Question Number 163428 Answers: 0 Comments: 2

jusgifier la convergence de ∫_0 ^1 ln(1−x^2 )dx

$${jusgifier}\:{la}\:{convergence}\:{de}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 163414 Answers: 1 Comments: 0

∫(dx/( (√(cosx sin^3 x))+(√(sinx cos^3 x))))

$$\int\frac{\boldsymbol{{dx}}}{\:\sqrt{\boldsymbol{{cosx}}\:\boldsymbol{{sin}}^{\mathrm{3}} \boldsymbol{{x}}}+\sqrt{\boldsymbol{{sinx}}\:\boldsymbol{{cos}}^{\mathrm{3}} \boldsymbol{{x}}}} \\ $$

Question Number 163413 Answers: 0 Comments: 3

Question Number 163408 Answers: 1 Comments: 0

((1+(2/9)(√(21))))^(1/3) +((1−(2/9)(√(21))))^(1/3) =?

$$\sqrt[{\mathrm{3}}]{\mathrm{1}+\frac{\mathrm{2}}{\mathrm{9}}\sqrt{\mathrm{21}}}+\sqrt[{\mathrm{3}}]{\mathrm{1}−\frac{\mathrm{2}}{\mathrm{9}}\sqrt{\mathrm{21}}}=? \\ $$

Question Number 163402 Answers: 1 Comments: 0

∫_0 ^1 (x−1)^(10) (x−3)^3 dx

$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \left(\boldsymbol{{x}}−\mathrm{1}\right)^{\mathrm{10}} \left(\boldsymbol{{x}}−\mathrm{3}\right)^{\mathrm{3}} \boldsymbol{{dx}} \\ $$

Question Number 163411 Answers: 0 Comments: 0

Question Number 163400 Answers: 2 Comments: 0

prove Ω= ∫_0 ^( ∞) cot^( −1) (1+x^( 2) )=((√((1/( (√2)))−(1/2))) ) π

$$ \\ $$$$\:\:\:\:\:{prove}\: \\ $$$$\:\:\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\infty} {cot}^{\:−\mathrm{1}} \left(\mathrm{1}+{x}^{\:\mathrm{2}} \right)=\left(\sqrt{\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}−\frac{\mathrm{1}}{\mathrm{2}}}\:\right)\:\:\pi \\ $$$$ \\ $$

Question Number 163397 Answers: 0 Comments: 5

Question Number 163396 Answers: 0 Comments: 0

if a and b are positive numbers then Σ (an + b)^(-p) converges if p>1 and diverges if p≤1

$$\mathrm{if}\:\:\boldsymbol{\mathrm{a}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{b}}\:\:\mathrm{are}\:\mathrm{positive}\:\mathrm{numbers} \\ $$$$\mathrm{then}\:\:\Sigma\:\left(\mathrm{an}\:+\:\mathrm{b}\right)^{-\boldsymbol{\mathrm{p}}} \:\:\mathrm{converges}\:\mathrm{if}\:\:\boldsymbol{\mathrm{p}}>\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{diverges}\:\mathrm{if}\:\:\boldsymbol{\mathrm{p}}\leqslant\mathrm{1} \\ $$

Question Number 163393 Answers: 1 Comments: 0

Question Number 163386 Answers: 1 Comments: 0

lim_(x→−∞) ((1−x^3 ))^(1/3) −((x^4 −1))^(1/4)

$$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\sqrt[{\mathrm{3}}]{\mathrm{1}−{x}^{\mathrm{3}} }−\sqrt[{\mathrm{4}}]{{x}^{\mathrm{4}} −\mathrm{1}} \\ $$

Question Number 163385 Answers: 1 Comments: 0

Question Number 163384 Answers: 2 Comments: 0

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