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Question Number 64729    Answers: 0   Comments: 0

Question Number 64728    Answers: 0   Comments: 0

Question Number 64726    Answers: 0   Comments: 0

Question Number 64709    Answers: 1   Comments: 1

Question Number 64702    Answers: 1   Comments: 0

Question Number 64697    Answers: 1   Comments: 0

i need some help here. An object of mass m falls from a height h_1 and rebound to a height of h_2 . write an expression for its momentum.

$${i}\:{need}\:{some}\:{help}\:{here}.\: \\ $$$$\:{An}\:{object}\:{of}\:{mass}\:\:\:{m}\:\:\:{falls}\:{from}\:{a}\:{height}\:\:{h}_{\mathrm{1}} \:{and}\:{rebound} \\ $$$${to}\:{a}\:{height}\:{of}\:{h}_{\mathrm{2}} .\:{write}\:{an}\:{expression}\:{for}\:{its}\:{momentum}. \\ $$

Question Number 64698    Answers: 1   Comments: 4

Question Number 64688    Answers: 1   Comments: 0

Question Number 64687    Answers: 0   Comments: 1

Question Number 64686    Answers: 1   Comments: 0

Question Number 64677    Answers: 0   Comments: 4

let f(x) =∫_0 ^1 lnt ln(1−xt)dt with ∣x∣<1 1)determine a explicit form for f(x) 2) find also g(x) =∫_0 ^1 ((tlnt)/(1−xt))dt 3) give f^((n)) (x) at form of integral 4) calculate ∫_0 ^1 ln(t)ln(1−t)dt and ∫_0 ^1 ln(t)ln(2−t)dt 5) calculate ∫_0 ^1 ((tln(t))/(2−t)) dt .

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {lnt}\:{ln}\left(\mathrm{1}−{xt}\right){dt}\:\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right){determine}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{tlnt}}{\mathrm{1}−{xt}}{dt} \\ $$$$\left.\mathrm{3}\right)\:{give}\:{f}^{\left({n}\right)} \left({x}\right)\:{at}\:{form}\:{of}\:{integral} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({t}\right){ln}\left(\mathrm{1}−{t}\right){dt}\:\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{ln}\left({t}\right){ln}\left(\mathrm{2}−{t}\right){dt} \\ $$$$\left.\mathrm{5}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{tln}\left({t}\right)}{\mathrm{2}−{t}}\:{dt}\:. \\ $$

Question Number 64676    Answers: 0   Comments: 0

z^4 −12iz−100=0

$${z}^{\mathrm{4}} −\mathrm{12}{iz}−\mathrm{100}=\mathrm{0} \\ $$

Question Number 64662    Answers: 1   Comments: 3

∫(dx/((x^8 +x^4 +1)^2 )) ∫_(1/x) ^x ((ln(t))/(t^2 +1)) dt

$$\int\frac{{dx}}{\left({x}^{\mathrm{8}} +{x}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$\int_{\frac{\mathrm{1}}{{x}}} ^{{x}} \frac{{ln}\left({t}\right)}{{t}^{\mathrm{2}} +\mathrm{1}}\:{dt} \\ $$

Question Number 64652    Answers: 0   Comments: 2

calculate S_n =Σ_(k=0) ^n k (C_n ^k )^2

$${calculate}\:\:{S}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}\:\left({C}_{{n}} ^{{k}} \right)^{\mathrm{2}} \\ $$

Question Number 64651    Answers: 1   Comments: 1

calculate Σ_(k=1) ^n kC_n ^k 3^k interms of n

$${calculate}\:\sum_{{k}=\mathrm{1}} ^{{n}} {kC}_{{n}} ^{{k}} \:\mathrm{3}^{{k}} \:\:{interms}\:{of}\:{n} \\ $$

Question Number 64650    Answers: 0   Comments: 1

U_n is a sequence wich verify lim_(n→+∞) U_(n+1) −U_n =a calculate lim_(n→+∞) (U_n /n)

$${U}_{{n}} \:{is}\:{a}\:{sequence}\:{wich}\:{verify}\:{lim}_{{n}\rightarrow+\infty} {U}_{{n}+\mathrm{1}} −{U}_{{n}} ={a}\:\:\: \\ $$$${calculate}\:{lim}_{{n}\rightarrow+\infty} \:\frac{{U}_{{n}} }{{n}} \\ $$

Question Number 64649    Answers: 1   Comments: 1

calculate ∫_0 ^(2π) ((cosθ)/(5+3cosθ))dθ

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{cos}\theta}{\mathrm{5}+\mathrm{3}{cos}\theta}{d}\theta \\ $$

Question Number 64642    Answers: 0   Comments: 1

∫(dx)/e^x +x

$$\int\left({dx}\right)/{e}^{{x}} +{x} \\ $$

Question Number 64640    Answers: 1   Comments: 3

I = Σ_(n = 0) ^∞ (((− 1)^n )/(6n + 1))

$$\mathrm{I}\:\:=\:\:\underset{\mathrm{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\:\:\frac{\left(−\:\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{6n}\:+\:\mathrm{1}} \\ $$

Question Number 64635    Answers: 0   Comments: 1

1)calculate f(a) =∫_0 ^∞ ((arctan(αx))/(1+x^2 ))dx with α real 2) find the value of ∫_0 ^∞ ((arctan(2x))/(1+x^2 ))dx

$$\left.\mathrm{1}\right){calculate}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:\:{with}\:\alpha\:{real} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 64631    Answers: 1   Comments: 3

(√((1+2x(√(1−x^2 )))/2))+2x^2 =1 To solve in R

$$\sqrt{\frac{\mathrm{1}+\mathrm{2}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{\mathrm{2}}}+\mathrm{2}{x}^{\mathrm{2}} =\mathrm{1} \\ $$$$\mathrm{To}\:\mathrm{solve}\:\mathrm{in}\:\mathbb{R} \\ $$

Question Number 64625    Answers: 2   Comments: 3

Question Number 64619    Answers: 0   Comments: 2

show that ∫_(−α) ^α sinc(x)dx=∫_(−α) ^α sinc^2 (x)dx=Π

$${show}\:{that}\:\int_{−\alpha} ^{\alpha} {sinc}\left({x}\right){dx}=\int_{−\alpha} ^{\alpha} {sinc}^{\mathrm{2}} \left({x}\right){dx}=\Pi \\ $$

Question Number 64612    Answers: 0   Comments: 3

Question Number 64610    Answers: 0   Comments: 2

Question Number 64591    Answers: 0   Comments: 0

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