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Question Number 61449 Answers: 1 Comments: 1

Question Number 61425 Answers: 0 Comments: 1

Question Number 61424 Answers: 1 Comments: 0

Question Number 61412 Answers: 0 Comments: 2

Find the multinomial coefficient: ((( 9)),((3, 5, 1, 0)) )

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{multinomial}\:\mathrm{coefficient}:\:\:\:\:\:\begin{pmatrix}{\:\:\:\:\:\:\:\:\:\mathrm{9}}\\{\mathrm{3},\:\:\mathrm{5},\:\:\mathrm{1},\:\:\mathrm{0}}\end{pmatrix} \\ $$

Question Number 61408 Answers: 1 Comments: 0

∫_0 ^π (x/(tan^2 (x)−1)) dx

$$\int_{\mathrm{0}} ^{\pi} \frac{{x}}{{tan}^{\mathrm{2}} \left({x}\right)−\mathrm{1}}\:{dx} \\ $$

Question Number 61402 Answers: 0 Comments: 0

Question Number 61391 Answers: 0 Comments: 2

what is the best book for learning advanced calculus ?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{best}\:\mathrm{book}\:\mathrm{for}\:\mathrm{learning}\:\mathrm{advanced} \\ $$$$\mathrm{calculus}\:? \\ $$

Question Number 61388 Answers: 0 Comments: 5

calculate ∫_0 ^1 ((sin(lnx))/(lnx)) dx .

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{sin}\left({lnx}\right)}{{lnx}}\:{dx}\:. \\ $$

Question Number 61386 Answers: 0 Comments: 3

find the value of ∫_(−∞) ^(+∞) ((ln(1+x^2 ))/(1+x^2 )) dx

$${find}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{+\infty} \:\:\frac{{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx} \\ $$

Question Number 61378 Answers: 0 Comments: 0

Solve the differential equation: (dy/dx) = x^2 + y^2

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\:=\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \\ $$

Question Number 61377 Answers: 0 Comments: 0

Find the multinomial coefficient: ((( 9)),((3, 5, 1, 0)) )

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{multinomial}\:\mathrm{coefficient}:\:\:\:\:\:\:\begin{pmatrix}{\:\:\:\:\:\:\:\mathrm{9}}\\{\mathrm{3},\:\mathrm{5},\:\mathrm{1},\:\mathrm{0}}\end{pmatrix} \\ $$

Question Number 61363 Answers: 1 Comments: 0

Question Number 61349 Answers: 1 Comments: 7

Question Number 61347 Answers: 2 Comments: 1

Question Number 61343 Answers: 1 Comments: 0

Question Number 61335 Answers: 1 Comments: 0

Question Number 61329 Answers: 0 Comments: 2

let f(x) =(e^(−x) /(1+x)) sin(3x) 1) dtermine f^((n)) (x) and f^((n)) (0) 2) developp f at integr serie .

$${let}\:{f}\left({x}\right)\:=\frac{{e}^{−{x}} }{\mathrm{1}+{x}}\:{sin}\left(\mathrm{3}{x}\right) \\ $$$$\left.\mathrm{1}\right)\:{dtermine}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$

Question Number 61328 Answers: 0 Comments: 4

let f(a) =∫_0 ^1 ((sin(2x))/(1+ax^2 )) dx with ∣a∣<1 1) approximate f(a) by a polynom 2) find the value (perhaps not exact) of ∫_0 ^1 ((sin(2x))/(1+2x^2 )) dx 3) let g(a) = ∫_0 ^1 ((x^2 sin(2x))/((1+ax^2 )^2 )) dx approximat g(a) by a polynom 4) find the value of ∫_0 ^1 ((x^2 sin(2x))/((1+2x^2 )^2 )) dx .

$${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{ax}^{\mathrm{2}} }\:{dx}\:\:{with}\:\:\mid{a}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{approximate}\:{f}\left({a}\right)\:{by}\:{a}\:{polynom} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:\:\left({perhaps}\:{not}\:{exact}\right)\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }\:{dx} \\ $$$$\left.\mathrm{3}\right)\:{let}\:{g}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{x}^{\mathrm{2}} {sin}\left(\mathrm{2}{x}\right)}{\left(\mathrm{1}+{ax}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:\:\:{approximat}\:{g}\left({a}\right)\:{by}\:{a}\:{polynom} \\ $$$$\left.\mathrm{4}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{x}^{\mathrm{2}} {sin}\left(\mathrm{2}{x}\right)}{\left(\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:. \\ $$

Question Number 61327 Answers: 1 Comments: 0

Question Number 61326 Answers: 0 Comments: 4

find ∫_0 ^1 ((sinx)/(1+x^2 ))dx

$${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{sinx}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 61322 Answers: 1 Comments: 0

Question Number 61320 Answers: 1 Comments: 0

solve for x: x^4 −x=12

$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}}: \\ $$$$\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{x}}^{\mathrm{4}} −\boldsymbol{\mathrm{x}}=\mathrm{12} \\ $$

Question Number 61318 Answers: 1 Comments: 0

Question Number 61313 Answers: 0 Comments: 3

how to calculate lim_(n→+∞) 0.05^(0.05^(0.05^.^.^(.0.05) ) ) }n in a simple and fast way?

$$\left.{how}\:{to}\:{calculate}\:\underset{{n}\rightarrow+\infty} {\mathrm{lim}0}.\mathrm{05}^{\mathrm{0}.\mathrm{05}^{\mathrm{0}.\mathrm{05}^{.^{.^{.\mathrm{0}.\mathrm{05}} } } } } \right\}{n} \\ $$$${in}\:{a}\:{simple}\:{and}\:{fast}\:{way}? \\ $$

Question Number 61303 Answers: 2 Comments: 3

Question Number 61297 Answers: 0 Comments: 0

A container is 50% full of water at triple point phase . It′s Isolated and subjected to space system defining no gravity acting on the particles , Which state of matter is now more dominant , solid , liquid , or gas ? Calculate the intermolecular distances between simultaneous two distinct states of water.

$$\mathrm{A}\:\mathrm{container}\:\mathrm{is}\:\mathrm{50\%}\:\mathrm{full}\:\mathrm{of}\:\mathrm{water}\:\mathrm{at}\:\mathrm{triple}\:\mathrm{point} \\ $$$$\mathrm{phase}\:.\:\mathrm{It}'\mathrm{s}\:\mathrm{Isolated}\:\mathrm{and}\:\mathrm{subjected}\:\mathrm{to}\:\mathrm{space} \\ $$$$\mathrm{system}\:\mathrm{defining}\:\mathrm{no}\:\mathrm{gravity}\:\mathrm{acting}\:\mathrm{on}\:\mathrm{the}\: \\ $$$$\mathrm{particles}\:,\:\mathrm{Which}\:\mathrm{state}\:\mathrm{of}\:\mathrm{matter}\:\mathrm{is}\:\mathrm{now} \\ $$$$\mathrm{more}\:\mathrm{dominant}\:,\:\mathrm{solid}\:,\:\mathrm{liquid}\:,\:\mathrm{or}\:\mathrm{gas}\:? \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{intermolecular}\:\mathrm{distances} \\ $$$$\mathrm{between}\:\mathrm{simultaneous}\:\mathrm{two}\:\mathrm{distinct}\:\mathrm{states} \\ $$$$\mathrm{of}\:\mathrm{water}.\: \\ $$

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