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Question Number 163467    Answers: 1   Comments: 0

Question Number 163463    Answers: 1   Comments: 0

nature de la serie Ξ£_(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 π›Œ>0 fixed solve for (0;∞) the equation: 2a^2 cos((x/(2Ξ»)) - ((2Ξ»)/x)) = a^(x/π›Œ) + a^((4π›Œ)/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_(nβˆ’1) ^p ).

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

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(1βˆ’x^2 )dx

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

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) +((1βˆ’(2/9)(√(21))))^(1/3) =?

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

Question Number 163402    Answers: 1   Comments: 0

∫_0 ^1 (xβˆ’1)^(10) (xβˆ’3)^3 dx

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

Question Number 163411    Answers: 0   Comments: 0

Question Number 163400    Answers: 2   Comments: 0

prove Ξ©= ∫_0 ^( ∞) cot^( βˆ’1) (1+x^( 2) )=((√((1/( (√2)))βˆ’(1/2))) ) Ο€

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

Question Number 163397    Answers: 0   Comments: 5

Question Number 163396    Answers: 0   Comments: 0

if a and b are positive numbers then Ξ£ (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_(xβ†’βˆ’βˆž) ((1βˆ’x^3 ))^(1/3) βˆ’((x^4 βˆ’1))^(1/4)

$$\underset{{x}\rightarrowβˆ’\infty} {\mathrm{lim}}\sqrt[{\mathrm{3}}]{\mathrm{1}βˆ’{x}^{\mathrm{3}} }βˆ’\sqrt[{\mathrm{4}}]{{x}^{\mathrm{4}} βˆ’\mathrm{1}} \\ $$

Question Number 163385    Answers: 1   Comments: 0

Question Number 163384    Answers: 2   Comments: 0

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