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Question Number 201184    Answers: 1   Comments: 0

Question Number 201081    Answers: 4   Comments: 0

Question Number 201070    Answers: 1   Comments: 0

Un = Σ_(k=1) ^n (1/ ((n),(k) )) show that the sequence converges and determine the limit

$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{Un}\:=\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{\begin{pmatrix}{{n}}\\{{k}}\end{pmatrix}} \\ $$$$ \\ $$$${show}\:\:{that}\:{the}\:{sequence}\:{converges}\:{and} \\ $$$${determine}\:{the}\:{limit}\: \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 201065    Answers: 2   Comments: 1

Question Number 201047    Answers: 0   Comments: 0

Question Number 201044    Answers: 2   Comments: 0

Ω = ∫_0 ^( 1) ∫_0 ^( 1) (x−y )^2 sin^( 2) ( x+y )dxdy=?

$$ \\ $$$$\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \left({x}−{y}\:\right)^{\mathrm{2}} {sin}^{\:\mathrm{2}} \:\left(\:{x}+{y}\:\right){dxdy}=? \\ $$

Question Number 201041    Answers: 1   Comments: 0

4(33)7 4(24)6 5( ? )4 a)9 b)18 c)27 d)36

$$\mathrm{4}\left(\mathrm{33}\right)\mathrm{7} \\ $$$$\mathrm{4}\left(\mathrm{24}\right)\mathrm{6} \\ $$$$\mathrm{5}\left(\:?\:\right)\mathrm{4} \\ $$$$ \\ $$$$\left.{a}\left.\right)\left.\mathrm{9}\left.\:\:\:\:\:{b}\right)\mathrm{18}\:\:\:\:\:{c}\right)\mathrm{27}\:\:\:\:\:{d}\right)\mathrm{36} \\ $$

Question Number 201037    Answers: 1   Comments: 1

Question Number 201035    Answers: 2   Comments: 2

Question Number 201034    Answers: 0   Comments: 0

Question Number 201033    Answers: 4   Comments: 0

Question Number 201029    Answers: 0   Comments: 0

Question Number 201028    Answers: 0   Comments: 0

Question Number 201027    Answers: 1   Comments: 0

Question Number 201016    Answers: 0   Comments: 0

Question Number 201011    Answers: 0   Comments: 0

Prove that ∫_0 ^∞ ((2arctan((t/x)))/(e^(2𝛑t) −1))dt=In𝚪(x)−xIn(x)+x−(1/2)In(((2𝛑)/x)) Michael faraday

$$\boldsymbol{{Prove}}\:\boldsymbol{{that}} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{2}\boldsymbol{{arctan}}\left(\frac{\boldsymbol{{t}}}{\boldsymbol{{x}}}\right)}{\boldsymbol{{e}}^{\mathrm{2}\boldsymbol{\pi{t}}} −\mathrm{1}}\boldsymbol{{dt}}=\boldsymbol{{In}\Gamma}\left(\boldsymbol{{x}}\right)−\boldsymbol{{xIn}}\left(\boldsymbol{{x}}\right)+\boldsymbol{{x}}−\frac{\mathrm{1}}{\mathrm{2}}\boldsymbol{{In}}\left(\frac{\mathrm{2}\boldsymbol{\pi}}{\boldsymbol{{x}}}\right) \\ $$$$\boldsymbol{{Michael}}\:\boldsymbol{{faraday}} \\ $$

Question Number 201008    Answers: 1   Comments: 0

Question Number 201004    Answers: 2   Comments: 0

Question Number 200984    Answers: 3   Comments: 0

Question Number 200980    Answers: 1   Comments: 0

Question Number 200979    Answers: 1   Comments: 0

Question Number 200978    Answers: 3   Comments: 0

Question Number 200968    Answers: 0   Comments: 0

Question Number 200971    Answers: 1   Comments: 0

Question Number 200976    Answers: 4   Comments: 0

Question Number 200973    Answers: 0   Comments: 0

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