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Question Number 56942 Answers: 0 Comments: 0

find U_n =∫_1 ^n (([(√(x+1))]−[(√x)])/x^3 ) dx 2) find nature of the serie Σ U_n

$${find}\:\:{U}_{{n}} =\int_{\mathrm{1}} ^{{n}} \:\frac{\left[\sqrt{{x}+\mathrm{1}}\right]−\left[\sqrt{{x}}\right]}{{x}^{\mathrm{3}} }\:{dx} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma\:{U}_{{n}} \\ $$

Question Number 56935 Answers: 0 Comments: 1

1. calculate U_n =∫_0 ^∞ (x^3 −2x+1)e^(−n[x]) dx with n integr natural and n≥1 2. find nature of Σ U_n

$$\mathrm{1}.\:{calculate}\:\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\left({x}^{\mathrm{3}} −\mathrm{2}{x}+\mathrm{1}\right){e}^{−{n}\left[{x}\right]} {dx}\:\:{with}\:{n}\:{integr}\:{natural}\:{and}\:{n}\geqslant\mathrm{1} \\ $$$$\mathrm{2}.\:{find}\:{nature}\:{of}\:\Sigma\:{U}_{{n}} \\ $$

Question Number 56932 Answers: 1 Comments: 0

let f_n (t) =∫_0 ^∞ (dx/((x^2 +t^2 )^n )) with n from N and n≥1 1. find a explicit form of f_n (t) 2. what is the value of g_n (t)=∫_0 ^∞ ((t dx)/((x^2 +t^2 )^(n+1) )) ? 3. calculate ∫_0 ^∞ (dx/((x^2 +3)^4 )) and ∫_0 ^∞ (dx/((x^2 +16)^3 ))

$${let}\:{f}_{{n}} \left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)^{{n}} } \\ $$$${with}\:{n}\:{from}\:{N}\:{and}\:{n}\geqslant\mathrm{1} \\ $$$$\mathrm{1}.\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}_{{n}} \left({t}\right) \\ $$$$\mathrm{2}.\:{what}\:{is}\:{the}\:{value}\:{of} \\ $$$${g}_{{n}} \left({t}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{{t}\:{dx}}{\left({x}^{\mathrm{2}} +{t}^{\mathrm{2}} \right)^{{n}+\mathrm{1}} }\:? \\ $$$$\mathrm{3}.\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{4}} } \\ $$$${and}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{16}\right)^{\mathrm{3}} } \\ $$

Question Number 56931 Answers: 1 Comments: 1

calculate ∫_(−∞) ^(+∞) ((x^2 −1)/((x^2 −x+3)^2 ))dx

$${calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{3}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 56921 Answers: 1 Comments: 0

Given : f(xy)=f(x).f(y)∀x,yεR and f(0)≠0 then f(x)=?

$${Given}\:: \\ $$$${f}\left({xy}\right)={f}\left({x}\right).{f}\left({y}\right)\forall{x},{y}\epsilon\mathbb{R}\:{and}\:{f}\left(\mathrm{0}\right)\neq\mathrm{0} \\ $$$${then}\:{f}\left({x}\right)=? \\ $$

Question Number 56914 Answers: 3 Comments: 0

The shortest distance between the point ((3/2),0) and the curve y=(√x) ,(x>0) is ?

$${The}\:{shortest}\:{distance}\:{between}\:{the}\:{point} \\ $$$$\left(\frac{\mathrm{3}}{\mathrm{2}},\mathrm{0}\right)\:{and}\:{the}\:{curve}\:{y}=\sqrt{{x}}\:,\left({x}>\mathrm{0}\right)\:{is}\:? \\ $$

Question Number 56913 Answers: 1 Comments: 2

How many possible solution sets that satisfy x_1 + x_2 + x_3 + x_4 = 5 with 0 ≤ x_1 ≤ 3 0 ≤ x_2 ≤ 3 0 ≤ x_3 ≤ 2 0 ≤ x_4 ≤ 2

$$\mathrm{How}\:\mathrm{many}\:\mathrm{possible}\:\mathrm{solution}\:\mathrm{sets}\:\mathrm{that}\:\mathrm{satisfy}\: \\ $$$${x}_{\mathrm{1}} \:+\:{x}_{\mathrm{2}} \:+\:{x}_{\mathrm{3}} \:+\:{x}_{\mathrm{4}} \:=\:\mathrm{5} \\ $$$$\mathrm{with} \\ $$$$\mathrm{0}\:\leqslant\:{x}_{\mathrm{1}} \:\leqslant\:\mathrm{3}\:\: \\ $$$$\mathrm{0}\:\leqslant\:{x}_{\mathrm{2}} \:\leqslant\:\mathrm{3} \\ $$$$\mathrm{0}\:\leqslant\:{x}_{\mathrm{3}} \:\leqslant\:\mathrm{2} \\ $$$$\mathrm{0}\:\leqslant\:{x}_{\mathrm{4}} \:\leqslant\:\mathrm{2} \\ $$

Question Number 56912 Answers: 1 Comments: 4

If a and b are positive integers such that (1+ab) divides (a^2 +b^2 ) show that the integer ((a^2 +b^2 )/(1+ab)) must be a perfect square.

$$\mathrm{If}\:{a}\:\mathrm{and}\:{b}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\left(\mathrm{1}+{ab}\right)\:\mathrm{divides}\:\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right)\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{integer} \\ $$$$\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }{\mathrm{1}+{ab}}\:\mathrm{must}\:\mathrm{be}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square}. \\ $$

Question Number 56904 Answers: 1 Comments: 0

If α and β are the roots of of the equation 3x^2 −x−3=0, find thevalue of (α^2 −β^2 ) if α>β.

$$\mathrm{If}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{3x}^{\mathrm{2}} −\mathrm{x}−\mathrm{3}=\mathrm{0},\:\mathrm{find}\:\mathrm{thevalue}\:\mathrm{of}\:\left(\alpha^{\mathrm{2}} −\beta^{\mathrm{2}} \right) \\ $$$$\mathrm{if}\:\alpha>\beta. \\ $$

Question Number 56900 Answers: 1 Comments: 0

Question Number 56899 Answers: 1 Comments: 0

Let W be the subspace of R^4 generated by vector (1, − 2, 5, − 3), (2, 3, 1, − 4), (3, 8, − 3, − 5) find the basis and dimension of W.

$$\mathrm{Let}\:\:\mathrm{W}\:\:\mathrm{be}\:\mathrm{the}\:\mathrm{subspace}\:\mathrm{of}\:\:\mathbb{R}^{\mathrm{4}} \:\:\mathrm{generated}\:\mathrm{by}\:\mathrm{vector}\: \\ $$$$\left(\mathrm{1},\:−\:\mathrm{2},\:\mathrm{5},\:−\:\mathrm{3}\right),\:\:\:\:\left(\mathrm{2},\:\mathrm{3},\:\mathrm{1},\:−\:\mathrm{4}\right),\:\:\:\left(\mathrm{3},\:\mathrm{8},\:−\:\mathrm{3},\:−\:\mathrm{5}\right)\:\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{basis}\:\mathrm{and}\:\mathrm{dimension}\:\mathrm{of}\:\:\mathrm{W}. \\ $$

Question Number 56895 Answers: 0 Comments: 0

26/3/2019 4 years of blood Stop the war on Yemen

$$\mathrm{26}/\mathrm{3}/\mathrm{2019} \\ $$$$\mathrm{4}\:\boldsymbol{{years}}\:\boldsymbol{{of}}\:\boldsymbol{{blood}} \\ $$$$\boldsymbol{{Stop}}\:\boldsymbol{{the}}\:\boldsymbol{{war}}\:\boldsymbol{{on}}\:\boldsymbol{{Yemen}} \\ $$

Question Number 56890 Answers: 0 Comments: 0

d^2 y/dx^2 =x^2 y=0

$${d}^{\mathrm{2}} {y}/{dx}^{\mathrm{2}} ={x}^{\mathrm{2}} {y}=\mathrm{0} \\ $$

Question Number 56886 Answers: 1 Comments: 0

Σ_(r=0) ^n ^n C_r ((1+r log_e 10)/((1+log_e 10^n )^r )) equals

$$\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\:^{{n}} {C}_{{r}} \frac{\mathrm{1}+{r}\:\mathrm{log}_{{e}} \mathrm{10}}{\left(\mathrm{1}+\mathrm{log}_{{e}} \mathrm{10}^{{n}} \right)^{{r}} }\:\:\mathrm{equals} \\ $$

Question Number 56878 Answers: 1 Comments: 0

f(x)= ∣∣x∣−4∣ g(x)= (√(36−x^2 ))−3 Find points of intersection.

$$\mathrm{f}\left(\mathrm{x}\right)=\:\mid\mid\mathrm{x}\mid−\mathrm{4}\mid \\ $$$$\mathrm{g}\left(\mathrm{x}\right)=\:\sqrt{\mathrm{36}−\mathrm{x}^{\mathrm{2}} }−\mathrm{3} \\ $$$$\mathrm{Find}\:\mathrm{points}\:\mathrm{of}\:\mathrm{intersection}. \\ $$

Question Number 56874 Answers: 1 Comments: 0

Question Number 56897 Answers: 1 Comments: 1

Question Number 56864 Answers: 1 Comments: 3

Find the solution of recurrence relation a_n = 2a_(n−1) + 3a_(n−2) , with a_0 = 1, a_1 = 2

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{recurrence}\:\mathrm{relation} \\ $$$${a}_{{n}} \:=\:\mathrm{2}{a}_{{n}−\mathrm{1}} \:+\:\mathrm{3}{a}_{{n}−\mathrm{2}} ,\:\mathrm{with}\:{a}_{\mathrm{0}} \:=\:\mathrm{1},\:{a}_{\mathrm{1}} \:=\:\mathrm{2} \\ $$

Question Number 56861 Answers: 0 Comments: 2

At 20°C, the solubility of Methoxymethane in water is 71.0 g.L^(−1) , however, ethanol and water are miscible. Given that : • Ethanol : H_3 C−C−O • Methoxymethane : H_3 C−O−CH_3 • X(H)=2.2 , X(C)=2.6 , X(O)=3.4 Considering the polarity of these solvents and molecules, how do you explain the difference between the soulubility of ethanol and Methoxymethane in water ? Thank you

$$\mathrm{At}\:\mathrm{20}°\mathrm{C},\:\mathrm{the}\:\mathrm{solubility}\:\mathrm{of}\:\mathrm{Methoxymethane} \\ $$$$\mathrm{in}\:\mathrm{water}\:\mathrm{is}\:\mathrm{71}.\mathrm{0}\:\mathrm{g}.\mathrm{L}^{−\mathrm{1}} ,\:\mathrm{however},\:\mathrm{ethanol}\:\mathrm{and} \\ $$$$\mathrm{water}\:\mathrm{are}\:\mathrm{miscible}. \\ $$$$\: \\ $$$$\:\:\:\mathrm{Given}\:\mathrm{that}\:: \\ $$$$\bullet\:\:\:\:\:\mathrm{Ethanol}\::\:\mathrm{H}_{\mathrm{3}} \mathrm{C}−\mathrm{C}−\mathrm{O} \\ $$$$\bullet\:\:\:\:\:\mathrm{Methoxymethane}\::\:\mathrm{H}_{\mathrm{3}} \mathrm{C}−\mathrm{O}−\mathrm{CH}_{\mathrm{3}} \\ $$$$\bullet\:\:\:\:\:\mathcal{X}\left(\mathrm{H}\right)=\mathrm{2}.\mathrm{2}\:,\:\mathcal{X}\left(\mathrm{C}\right)=\mathrm{2}.\mathrm{6}\:,\:\mathcal{X}\left(\mathrm{O}\right)=\mathrm{3}.\mathrm{4} \\ $$$$\: \\ $$$$\mathrm{Considering}\:\mathrm{the}\:\mathrm{polarity}\:\mathrm{of}\:\mathrm{these}\:\mathrm{solvents} \\ $$$$\mathrm{and}\:\mathrm{molecules},\:\mathrm{how}\:\mathrm{do}\:\mathrm{you}\:\mathrm{explain}\:\mathrm{the} \\ $$$$\mathrm{difference}\:\mathrm{between}\:\mathrm{the}\:\mathrm{soulubility}\:\mathrm{of} \\ $$$$\mathrm{ethanol}\:\mathrm{and}\:\mathrm{Methoxymethane}\:\mathrm{in}\:\mathrm{water}\:? \\ $$$$\: \\ $$$$\mathrm{Thank}\:\mathrm{you} \\ $$

Question Number 56857 Answers: 0 Comments: 0

romi−romo=0 L.x_0 +G.y_n =L.x_n +G.y_0 L(x_0 −x_n )=G(y_0 −y_n ) y_0 =(L/G).(x_0 −x_n )+y_n y_0 =((100)/(200))(0.01−0.001)+0.0005 y_0 =0.005

$${romi}−{romo}=\mathrm{0} \\ $$$$\mathcal{L}.{x}_{\mathrm{0}} +\mathcal{G}.{y}_{{n}} =\mathcal{L}.{x}_{{n}} +\mathcal{G}.{y}_{\mathrm{0}} \\ $$$$\mathcal{L}\left({x}_{\mathrm{0}} −{x}_{{n}} \right)=\mathcal{G}\left({y}_{\mathrm{0}} −{y}_{{n}} \right) \\ $$$${y}_{\mathrm{0}} =\frac{\mathcal{L}}{\mathcal{G}}.\left({x}_{\mathrm{0}} −{x}_{{n}} \right)+{y}_{{n}} \\ $$$${y}_{\mathrm{0}} =\frac{\mathrm{100}}{\mathrm{200}}\left(\mathrm{0}.\mathrm{01}−\mathrm{0}.\mathrm{001}\right)+\mathrm{0}.\mathrm{0005} \\ $$$${y}_{\mathrm{0}} =\mathrm{0}.\mathrm{005} \\ $$$$ \\ $$

Question Number 56854 Answers: 0 Comments: 1

There was a post sime time back about not being able to backup or restore. Can anyone send the requirdd information if you faced the same problem?

$$\mathrm{There}\:\mathrm{was}\:\mathrm{a}\:\mathrm{post}\:\mathrm{sime}\:\mathrm{time}\:\mathrm{back} \\ $$$$\mathrm{about}\:\mathrm{not}\:\mathrm{being}\:\mathrm{able}\:\mathrm{to}\:\mathrm{backup} \\ $$$$\mathrm{or}\:\mathrm{restore}.\:\mathrm{Can}\:\mathrm{anyone}\:\mathrm{send}\:\mathrm{the}\:\mathrm{requirdd} \\ $$$$\mathrm{information}\:\mathrm{if}\:\mathrm{you}\:\mathrm{faced}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{problem}? \\ $$

Question Number 56852 Answers: 1 Comments: 0