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Question Number 210309    Answers: 0   Comments: 1

For what value of p does the series Σ_(n=1) ^∞ (e^n /((2+e^(2n) )^p )) converge

$${For}\:{what}\:{value}\:{of}\:{p}\:{does}\:{the}\:{series} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{e}^{{n}} }{\left(\mathrm{2}+{e}^{\mathrm{2}{n}} \right)^{{p}} }\:\:\:\:\:{converge} \\ $$

Question Number 210308    Answers: 3   Comments: 1

Evaluate ∫((2y^4 )/(y^3 −y^2 +y−1))dy

$${Evaluate}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\int\frac{\mathrm{2}{y}^{\mathrm{4}} }{{y}^{\mathrm{3}} −{y}^{\mathrm{2}} +{y}−\mathrm{1}}{dy} \\ $$

Question Number 210307    Answers: 3   Comments: 0

∫((x^2 −1)/((x^2 +1)((√(1+x^4 )) )))

$$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left(\sqrt{\mathrm{1}+{x}^{\mathrm{4}} }\:\right)} \\ $$$$ \\ $$

Question Number 210297    Answers: 0   Comments: 0

Prove the theorem. A non empty subset W of a vector space V(F) is the subset of V if and only if αW_1 +βW_2 ∈W ∀α,β ∈ F and W_1 ,W_2 ∈W

$${Prove}\:{the}\:{theorem}. \\ $$$${A}\:{non}\:{empty}\:{subset}\:{W}\:\:{of}\:{a}\:{vector}\:{space}\:{V}\left({F}\right) \\ $$$${is}\:{the}\:{subset}\:{of}\:{V}\:\:{if}\:\:{and}\:{only}\:{if} \\ $$$$\alpha{W}_{\mathrm{1}} +\beta{W}_{\mathrm{2}} \:\in{W}\:\:\forall\alpha,\beta\:\in\:{F}\:\:{and}\:{W}_{\mathrm{1}} ,{W}_{\mathrm{2}} \:\in{W} \\ $$

Question Number 210298    Answers: 0   Comments: 0

For the given system of simultaneous linear equation 2x_1 −2x_2 +3x_3 +4x_4 −x_5 =0 −x_3 −2x_4 +3x_5 =0 −x_1 +x_2 +2x_3 +5x_4 +2x_5 =0 x_1 −x_2 +2x_3 +3x_4 =0 (a)Write the augmented matrix and convert it into echelon form (b)Hence find all the solution

$${For}\:{the}\:{given}\:{system}\:{of}\:{simultaneous}\: \\ $$$${linear}\:{equation} \\ $$$$\mathrm{2}{x}_{\mathrm{1}} −\mathrm{2}{x}_{\mathrm{2}} +\mathrm{3}{x}_{\mathrm{3}} +\mathrm{4}{x}_{\mathrm{4}} −{x}_{\mathrm{5}} =\mathrm{0} \\ $$$$−{x}_{\mathrm{3}} −\mathrm{2}{x}_{\mathrm{4}} +\mathrm{3}{x}_{\mathrm{5}} =\mathrm{0} \\ $$$$−{x}_{\mathrm{1}} +{x}_{\mathrm{2}} +\mathrm{2}{x}_{\mathrm{3}} +\mathrm{5}{x}_{\mathrm{4}} +\mathrm{2}{x}_{\mathrm{5}} =\mathrm{0} \\ $$$${x}_{\mathrm{1}} −{x}_{\mathrm{2}} +\mathrm{2}{x}_{\mathrm{3}} +\mathrm{3}{x}_{\mathrm{4}} =\mathrm{0} \\ $$$$\left({a}\right){Write}\:{the}\:{augmented}\:\:{matrix}\:{and}\:{convert} \\ $$$${it}\:{into}\:{echelon}\:{form} \\ $$$$\left({b}\right){Hence}\:{find}\:{all}\:{the}\:{solution} \\ $$$$ \\ $$

Question Number 210295    Answers: 0   Comments: 1

Question Number 210292    Answers: 1   Comments: 1

Question Number 210291    Answers: 1   Comments: 0

Question Number 210290    Answers: 1   Comments: 0

Question Number 210289    Answers: 1   Comments: 0

Question Number 210265    Answers: 1   Comments: 11

If we observe when light source illuminates the surface of an object lets say its a sphere(football) ,the area visible zone decreases as the light source comes near the surface.So calculate rate of change visible area when light source is coming towards the object or moving away from the object.And in the case of earth find the equation in function of time If the light object is coming from space towards earth, express that expression in the function of time

$${If}\:{we}\:{observe}\:{when}\:{light}\:{source}\: \\ $$$${illuminates}\:{the}\:{surface}\:{of}\:{an}\:{object} \\ $$$${lets}\:{say}\:{its}\:{a}\:{sphere}\left({football}\right)\:,{the}\:{area} \\ $$$${visible}\:{zone}\:{decreases}\:{as}\:{the}\:{light}\:{source} \\ $$$${comes}\:{near}\:{the}\:{surface}.{So}\:\:{calculate}\:{rate}\:{of}\:{change} \\ $$$${visible}\:{area}\:{when}\:{light}\:{source}\:{is}\:{coming} \\ $$$${towards}\:{the}\:{object}\:{or}\:{moving}\:{away}\: \\ $$$${from}\:{the}\:{object}.{And}\:{in}\:{the}\:{case}\:{of}\:{earth} \\ $$$${find}\:{the}\:{equation}\:{in}\:{function}\:{of}\:{time} \\ $$$${If}\:{the}\:{light}\:{object}\:{is}\:{coming}\:{from}\:{space} \\ $$$${towards}\:{earth},\:{express}\:{that}\:{expression} \\ $$$${in}\:{the}\:{function}\:{of}\:{time} \\ $$$$ \\ $$$$ \\ $$

Question Number 210263    Answers: 2   Comments: 0

Question Number 210261    Answers: 2   Comments: 0

show that ((sinAcosA−sinBcosB)/(cos^2 A−sin^2 B))=tan(A−B)

$$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}} \\ $$$$\frac{\boldsymbol{\mathrm{sinAcosA}}−\boldsymbol{\mathrm{sinBcosB}}}{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \boldsymbol{\mathrm{A}}−\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{\mathrm{B}}}=\boldsymbol{\mathrm{tan}}\left(\boldsymbol{\mathrm{A}}−\boldsymbol{\mathrm{B}}\right) \\ $$

Question Number 210248    Answers: 1   Comments: 0

Question Number 210236    Answers: 2   Comments: 0

Question Number 210235    Answers: 2   Comments: 2

Question Number 210234    Answers: 2   Comments: 2

Question Number 210233    Answers: 2   Comments: 0

Question Number 210231    Answers: 0   Comments: 1

Resoudre dans R { ((acos x−bsin x=c (x≠0))),((sin ((1/(sin x))) =d (−1≤d≤+1))) :}

$$\mathrm{Resoudre}\:\boldsymbol{\mathrm{dans}}\:\mathbb{R} \\ $$$$\begin{cases}{\boldsymbol{\mathrm{a}}\mathrm{cos}\:\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{b}}\mathrm{sin}\:\boldsymbol{\mathrm{x}}=\boldsymbol{\mathrm{c}}\:\:\:\:\:\left(\boldsymbol{\mathrm{x}}\neq\mathrm{0}\right)}\\{\mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{sin}\:\boldsymbol{\mathrm{x}}}\right)\:\:\:\:\:\:\:\:\:=\boldsymbol{\mathrm{d}}\:\:\:\:\left(−\mathrm{1}\leqslant\boldsymbol{\mathrm{d}}\leqslant+\mathrm{1}\right)}\end{cases} \\ $$$$ \\ $$

Question Number 210208    Answers: 4   Comments: 0

∫_0 ^1 e^e^e^x e^e^x e^x dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{{e}^{{e}^{{x}} } } \:{e}^{{e}^{{x}} } \:{e}^{{x}} {dx} \\ $$$$ \\ $$

Question Number 210206    Answers: 0   Comments: 0

Ω=∫_(1/e) ^e (dx/((1+x^2 )(1+xlog^7 x)))

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{\frac{\mathrm{1}}{{e}}} ^{{e}} \frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}\mathrm{log}\:^{\mathrm{7}} {x}\right)} \\ $$$$ \\ $$

Question Number 210229    Answers: 3   Comments: 0

Question Number 210228    Answers: 0   Comments: 0

Question Number 210227    Answers: 0   Comments: 0

Question Number 210369    Answers: 0   Comments: 0

Question Number 210194    Answers: 0   Comments: 1

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