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Question Number 160058 Answers: 1 Comments: 2

Find n so that ((a^(n+1) +b^(n+1) )/(a^n +b^n )) may be the arithmetic mean between a and b.

$${Find}\:{n}\:{so}\:{that}\:\frac{{a}^{{n}+\mathrm{1}} +{b}^{{n}+\mathrm{1}} }{{a}^{{n}} +{b}^{{n}} }\:{may}\:{be} \\ $$$${the}\:{arithmetic}\:{mean}\:{between}\:{a} \\ $$$${and}\:{b}. \\ $$

Question Number 160052 Answers: 1 Comments: 0

find Φ(k)=Σ_(n=1) ^∞ (n^k /(n!)) with k≥1.

$${find}\:\Phi\left({k}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}^{{k}} }{{n}!}\:{with}\:{k}\geqslant\mathrm{1}. \\ $$

Question Number 160050 Answers: 1 Comments: 0

Question Number 160048 Answers: 0 Comments: 0

Prove that: ∫_( 0) ^( 1) ((x sin^(-1) x)/(1 + sin^(-1) x)) dx < (1/4)

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\frac{\mathrm{x}\:\mathrm{sin}^{-\mathrm{1}} \:\mathrm{x}}{\mathrm{1}\:+\:\mathrm{sin}^{-\mathrm{1}} \:\mathrm{x}}\:\mathrm{dx}\:<\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$

Question Number 160045 Answers: 0 Comments: 0

Question Number 160036 Answers: 0 Comments: 0

Question Number 160035 Answers: 0 Comments: 0

Question Number 160025 Answers: 0 Comments: 1

Question Number 160023 Answers: 0 Comments: 0

Question Number 160014 Answers: 1 Comments: 2

Question Number 160013 Answers: 0 Comments: 1

∫(1/(4sin x+3cos x))dx evaluate

$$\int\frac{\mathrm{1}}{\mathrm{4}{sin}\:{x}+\mathrm{3}{cos}\:{x}}{dx} \\ $$$${evaluate} \\ $$

Question Number 160009 Answers: 1 Comments: 0

Find: lim_(n→∞) (((n!))^(1/n) ∙∫_((1/1^2 ) + (1/2^2 ) + ... + (1/n^2 )) ^( (𝛑^2 /6)) e^x^2 dx)

$$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\left(\sqrt[{\boldsymbol{\mathrm{n}}}]{\mathrm{n}!}\:\centerdot\underset{\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }\:+\:...\:+\:\frac{\mathrm{1}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }} {\overset{\:\frac{\boldsymbol{\pi}^{\mathrm{2}} }{\mathrm{6}}} {\int}}\:\mathrm{e}^{\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \:\mathrm{dx}\right) \\ $$

Question Number 160008 Answers: 2 Comments: 2

x_1 =3 ; n(x_1 +x_2 +...+x_n )=x_n ; n∈N ; n≥1 Find: Ω =Σ_(n=1) ^∞ (-1)^(n+1) x_n

$$\mathrm{x}_{\mathrm{1}} =\mathrm{3}\:;\:\mathrm{n}\left(\mathrm{x}_{\mathrm{1}} +\mathrm{x}_{\mathrm{2}} +...+\mathrm{x}_{\boldsymbol{\mathrm{n}}} \right)=\mathrm{x}_{\boldsymbol{\mathrm{n}}} \:;\:\mathrm{n}\in\mathbb{N}\:;\:\mathrm{n}\geqslant\mathrm{1} \\ $$$$\mathrm{Find}: \\ $$$$\Omega\:=\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\left(-\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}+\mathrm{1}} \:\mathrm{x}_{\boldsymbol{\mathrm{n}}} \\ $$

Question Number 160007 Answers: 0 Comments: 0

Find: lim_(n→∞) (n(((1 + (1/n))^n - e - 1)^n - e^(- (e/2)) ))

$$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{n}\left(\left(\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{n}}\right)^{\boldsymbol{\mathrm{n}}} -\:\mathrm{e}\:-\:\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}} -\:\mathrm{e}^{-\:\frac{\mathrm{e}}{\mathrm{2}}} \right)\right) \\ $$$$ \\ $$

Question Number 160006 Answers: 0 Comments: 2

Evaluate: lim_(n→∞) ∫_n ^(n+1) e^(1/x) dx = ?

$$\mathrm{Evaluate}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\underset{\boldsymbol{\mathrm{n}}} {\overset{\boldsymbol{\mathrm{n}}+\mathrm{1}} {\int}}\:\mathrm{e}^{\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}} \:\mathrm{dx}\:=\:? \\ $$$$ \\ $$

Question Number 159999 Answers: 1 Comments: 0

Question Number 159994 Answers: 1 Comments: 0

montrer que le quotient d′un nombe rationnel et dun nombre irrationnel est irrationnel

$$ \\ $$$$\mathrm{montrer}\:\mathrm{que}\:\mathrm{le}\:\mathrm{quotient}\:\mathrm{d}'\mathrm{un} \\ $$$$\mathrm{nombe}\:\mathrm{rationnel}\:\mathrm{et}\:\mathrm{dun}\:\mathrm{nombre}\: \\ $$$$\mathrm{irr}{a}\mathrm{tionnel}\:\mathrm{est}\:\mathrm{irrationnel} \\ $$

Question Number 159973 Answers: 0 Comments: 6

Can anyone please resolve the Q 159787 in details..

$${Can}\:{anyone}\:{please}\:{resolve}\:{the} \\ $$$${Q}\:\mathrm{159787}\:{in}\:{details}.. \\ $$

Question Number 159966 Answers: 0 Comments: 2

a y=(√(x+(√(x+(√(x+.....)))))) b y=(√(x(√(x(√(x(√(x.....)))))))) find (dy/dx)

$${a}\:\:\:\:{y}=\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+.....}}} \\ $$$${b}\:\:\:\:\:{y}=\sqrt{{x}\sqrt{{x}\sqrt{{x}\sqrt{{x}.....}}}} \\ $$$${find}\:\frac{{dy}}{{dx}} \\ $$

Question Number 159962 Answers: 0 Comments: 0

show me: these are the cauchy criterion. please 1.(((n+1)/n)) 2. (1+(1/(2!))+(1/(3!))+...+(1/(n!))) 3. ((−1)^n ) 4. n+(((−1)^n )/n) 5.(1nm)

$${show}\:{me}:\:{these}\:{are}\:{the}\:{cauchy}\:{criterion}.\:{please} \\ $$$$\mathrm{1}.\left(\frac{{n}+\mathrm{1}}{{n}}\right) \\ $$$$\mathrm{2}.\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}!}+\frac{\mathrm{1}}{\mathrm{3}!}+...+\frac{\mathrm{1}}{{n}!}\right) \\ $$$$\mathrm{3}.\:\left(\left(−\mathrm{1}\right)^{{n}} \right) \\ $$$$\mathrm{4}.\:{n}+\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}} \\ $$$$\mathrm{5}.\left(\mathrm{1}{nm}\right) \\ $$$$ \\ $$

Question Number 159961 Answers: 4 Comments: 0

if x + (1/x) = 2(√5) then find the value of ((x(x^6 − 1))/(x^8 − 1))

$$\mathrm{if}\:{x}\:+\:\frac{\mathrm{1}}{{x}}\:=\:\mathrm{2}\sqrt{\mathrm{5}}\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{{x}\left({x}^{\mathrm{6}} \:−\:\mathrm{1}\right)}{{x}^{\mathrm{8}} \:−\:\mathrm{1}} \\ $$

Question Number 159960 Answers: 1 Comments: 0

∫_0 ^( 1) ((3x^3 −x^2 +2x−4)/( (√(x^2 −3x+2)))) dx =?

$$\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{3}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{4}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}}}\:{dx}\:=?\: \\ $$

Question Number 159958 Answers: 1 Comments: 3

find the area and perimeter of ((x/a))^(2/3) +((y/b))^(2/3) =1

$${find}\:{the}\:{area}\:{and}\:{perimeter}\:{of} \\ $$$$\left(\frac{\boldsymbol{{x}}}{\boldsymbol{{a}}}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} +\left(\frac{\boldsymbol{{y}}}{\boldsymbol{{b}}}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} =\mathrm{1} \\ $$

Question Number 159944 Answers: 0 Comments: 4

Question Number 159943 Answers: 1 Comments: 0

Question Number 159942 Answers: 0 Comments: 0

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