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Question Number 27613    Answers: 1   Comments: 1

find the value of ∫_0 ^∞ e^(−[x] −x) dx .

$${find}\:{the}\:{value}\:{of}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\left[{x}\right]\:−{x}} {dx}\:\:. \\ $$

Question Number 27612    Answers: 1   Comments: 0

∫(1/(3+cos^2 x))dx

$$\int\frac{\mathrm{1}}{\mathrm{3}+{cos}^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 27611    Answers: 1   Comments: 0

∫(1/(2sin^2 x + 4cos^2 x))dx

$$\int\frac{\mathrm{1}}{\mathrm{2sin}\:^{\mathrm{2}} {x}\:+\:\mathrm{4cos}\:^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 27609    Answers: 0   Comments: 0

Δ=(√(m×φ)) Δ=mass gap m=mass φ=phi calculate phi to the same number of decimal places as the mass. use the mass of an electron

$$\Delta=\sqrt{{m}×\phi} \\ $$$$\Delta={mass}\:{gap} \\ $$$${m}={mass} \\ $$$$\phi={phi} \\ $$$${calculate}\:{phi}\:{to}\:{the}\:{same}\:{number}\:{of}\: \\ $$$${decimal}\:{places}\:{as}\:{the}\:{mass}. \\ $$$${use}\:{the}\:{mass}\:{of}\:{an}\:{electron} \\ $$

Question Number 27608    Answers: 0   Comments: 5

f(x) = ln(x +(√(x^2 +1))) find f^(−1) (x) plzz help

$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{ln}\left(\mathrm{x}\:+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\right) \\ $$$$ \\ $$$$\mathrm{find}\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right) \\ $$$$\mathrm{plzz}\:\mathrm{help} \\ $$

Question Number 27607    Answers: 0   Comments: 0

Question Number 27606    Answers: 0   Comments: 0

Question Number 27605    Answers: 1   Comments: 0

Question Number 27604    Answers: 0   Comments: 1

Let S_n =(1/1^3 ) + ((1+2)/(1^3 +2^3 )) +...+((1+2+...+n)/(1^3 +2^3 +...+n^3 )); n=1,2,3,.. Then S_n is greater than

$$\mathrm{Let}\: \\ $$$${S}_{{n}} =\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{3}} }\:+\:\frac{\mathrm{1}+\mathrm{2}}{\mathrm{1}^{\mathrm{3}} +\mathrm{2}^{\mathrm{3}} }\:+...+\frac{\mathrm{1}+\mathrm{2}+...+{n}}{\mathrm{1}^{\mathrm{3}} +\mathrm{2}^{\mathrm{3}} +...+{n}^{\mathrm{3}} };\:{n}=\mathrm{1},\mathrm{2},\mathrm{3},.. \\ $$$$\mathrm{Then}\:{S}_{{n}} \:\mathrm{is}\:\mathrm{greater}\:\mathrm{than} \\ $$

Question Number 27601    Answers: 0   Comments: 0

f fonction numerical increasing on ]0,1] and ∫_0 ^1 f(t)dt converges prove that lim_(n−>∝) (1/n) Σ_(k=1) ^n f((k/n)) = ∫_0 ^1 f(t)dt .

$$\left.{f}\left.\:{fonction}\:{numerical}\:{increasing}\:{on}\:\right]\mathrm{0},\mathrm{1}\right]\:{and} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({t}\right){dt}\:{converges}\:{prove}\:{that}\:\:{lim}_{{n}−>\propto} \:\:\frac{\mathrm{1}}{{n}}\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{f}\left(\frac{{k}}{{n}}\right) \\ $$$$=\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({t}\right){dt}\:\:. \\ $$

Question Number 27600    Answers: 0   Comments: 1

find ∫_0 ^π (t/(2+sint)) dt

$${find}\:\:\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{t}}{\mathrm{2}+{sint}}\:{dt} \\ $$

Question Number 27599    Answers: 0   Comments: 0

let give the equation x^6 −x−1=0 by using Newton methodfind the approximate value of the real?root for this equation.

$${let}\:{give}\:{the}\:{equation}\:\:{x}^{\mathrm{6}} −{x}−\mathrm{1}=\mathrm{0}\:\:{by}\:{using}\:{Newton}\:{methodfind} \\ $$$${the}\:{approximate}\:{value}\:{of}\:{the}\:{real}?{root}\:\:{for}\:{this}\:{equation}. \\ $$

Question Number 27598    Answers: 0   Comments: 1

find ∫∫∫_D (x^2 +y^2 )dxdxy with D={x,y,z)∈R^3 /x^2 +y^2 +z^2 ≤1 and z≥0 }

$${find}\:\int\int\int_{{D}} \left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){dxdxy}\:\:\:{with} \\ $$$$\left.{D}=\left\{{x},{y},{z}\right)\in{R}^{\mathrm{3}} \:\:\:/{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \:\leqslant\mathrm{1}\:\:{and}\:{z}\geqslant\mathrm{0}\:\right\} \\ $$

Question Number 27597    Answers: 0   Comments: 0

find ∫ ((√(cos(2x)))/(cosx)) dx.

$${find}\:\int\:\:\frac{\sqrt{{cos}\left(\mathrm{2}{x}\right)}}{{cosx}}\:{dx}. \\ $$

Question Number 27596    Answers: 0   Comments: 1

find ∫ ^3 (√( x^2 −x^3 )) dx

$${find}\:\:\int\:\:\:^{\mathrm{3}} \sqrt{\:{x}^{\mathrm{2}} −{x}^{\mathrm{3}} }\:\:{dx} \\ $$

Question Number 27595    Answers: 0   Comments: 1

find ∫∫_D xy(√( x^2 +y^2 )) dxdy with D={ (x,y)∈R^2 / x^2 +2y^2 ≤1 ,x≥0 ,y ≥0}

$${find}\:\:\int\int_{{D}} \:\:{xy}\sqrt{\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:\:{dxdy}\:\:\:{with} \\ $$$${D}=\left\{\:\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:{x}^{\mathrm{2}} \:+\mathrm{2}{y}^{\mathrm{2}} \:\leqslant\mathrm{1}\:\:,{x}\geqslant\mathrm{0}\:,{y}\:\geqslant\mathrm{0}\right\} \\ $$

Question Number 27603    Answers: 0   Comments: 1

Find the value of i^i ?

$${Find}\:\:{the}\:{value}\:{of}\:\:\:{i}^{{i}} \:\:? \\ $$$$ \\ $$$$ \\ $$

Question Number 27587    Answers: 1   Comments: 1

divide 12x(8x−20) by 4(2x−5)

$$\mathrm{divide}\:\mathrm{12x}\left(\mathrm{8x}−\mathrm{20}\right)\:\mathrm{by}\:\mathrm{4}\left(\mathrm{2x}−\mathrm{5}\right) \\ $$

Question Number 27581    Answers: 1   Comments: 0

If f(x)=∫(4x−x^2 )dx f(3)=22, find f(x)

$$\mathrm{If}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\int\left(\mathrm{4}\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} \right)\boldsymbol{\mathrm{dx}} \\ $$$$\mathrm{f}\left(\mathrm{3}\right)=\mathrm{22},\:\mathrm{find}\:{f}\left(\mathrm{x}\right) \\ $$

Question Number 27580    Answers: 1   Comments: 0

Simplify (1/(1−cos a)) + (1/(1+cos a)) and leave the answer in the form⇒ sin a

$$\mathrm{Simplify}\:\frac{\mathrm{1}}{\mathrm{1}−\mathrm{cos}\:\mathrm{a}}\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cos}\:\mathrm{a}} \\ $$$$\mathrm{and}\:\mathrm{leave}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{the}\: \\ $$$$\mathrm{form}\Rightarrow\:\:\:\mathrm{sin}\:\mathrm{a} \\ $$

Question Number 27579    Answers: 1   Comments: 0

A circle with center (−3,1) passes through the point (3,1). Find it′s equation

$$\mathrm{A}\:\mathrm{circle}\:\mathrm{with}\:\mathrm{center}\:\left(−\mathrm{3},\mathrm{1}\right) \\ $$$$\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{point}\: \\ $$$$\left(\mathrm{3},\mathrm{1}\right).\:\mathrm{Find}\:\mathrm{it}'\mathrm{s}\:\mathrm{equation} \\ $$

Question Number 27578    Answers: 0   Comments: 1

if f(x)=((2x−3)/((x^2 −1)(x+2))) 1. Find the value for which f(x) is undefied. 2.Express f(x) in partial fraction

$$\mathrm{if}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{2x}−\mathrm{3}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{x}+\mathrm{2}\right)} \\ $$$$\mathrm{1}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{for}\:\mathrm{which}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{undefied}. \\ $$$$\mathrm{2}.\mathrm{Express}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{in}\:\mathrm{partial}\:\mathrm{fraction} \\ $$

Question Number 27577    Answers: 0   Comments: 0

find the equation of the line of the stationary point y=x^2 (x−3) and the distance between them

$$\mathrm{find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{stationary}\:\mathrm{point}\: \\ $$$$\boldsymbol{\mathrm{y}}=\boldsymbol{\mathrm{x}}^{\mathrm{2}} \left(\boldsymbol{\mathrm{x}}−\mathrm{3}\right)\: \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{them} \\ $$

Question Number 27594    Answers: 0   Comments: 1

solve the differencial equation (1−x^2 )y^′ −xy =1 .

$${solve}\:{the}\:\:{differencial}\:{equation} \\ $$$$\left(\mathrm{1}−{x}^{\mathrm{2}} \right){y}^{'} \:−{xy}\:=\mathrm{1}\:\:\:. \\ $$

Question Number 27568    Answers: 1   Comments: 0

carol is 6 times as old as her nephew Hondo.Baby is 22 years yonger than her aunt carol.In four years carol′s age will be twice the sum of Hondo′s and Baby′s age.How old is each perso n now?

$${carol}\:{is}\:\mathrm{6}\:{times}\:{as}\:{old}\:{as}\:{her}\:{nephew} \\ $$$${Hondo}.{Baby}\:{is}\:\mathrm{22}\:{years}\:{yonger}\:{than} \\ $$$${her}\:{aunt}\:{carol}.{In}\:{four}\:{years}\:{carol}'{s} \\ $$$${age}\:{will}\:{be}\:{twice}\:{the}\:{sum}\:{of}\:{Hondo}'{s} \\ $$$${and}\:{Baby}'{s}\:{age}.{How}\:{old}\:{is}\:{each}\:{perso} \\ $$$${n}\:{now}? \\ $$

Question Number 27567    Answers: 0   Comments: 0

f(x)=3x^2 (a)Find the critical number (b)Find the interval on which f increase and decrese (c)Find the local extrem value of f (d)using the 2^(nd) derivative, find local extrem

$$\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{3x}^{\mathrm{2}} \\ $$$$\left(\mathrm{a}\right)\mathrm{Find}\:\mathrm{the}\:\mathrm{critical}\:\mathrm{number} \\ $$$$\left(\mathrm{b}\right)\mathrm{Find}\:\mathrm{the}\:\mathrm{interval}\:\mathrm{on}\:\mathrm{which}\:\mathrm{f} \\ $$$$\mathrm{increase}\:\mathrm{and}\:\mathrm{decrese} \\ $$$$\left(\mathrm{c}\right)\mathrm{Find}\:\mathrm{the}\:\mathrm{local}\:\mathrm{extrem}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f} \\ $$$$\left(\mathrm{d}\right)\mathrm{using}\:\mathrm{the}\:\mathrm{2}^{\mathrm{nd}} \:\mathrm{derivative}, \\ $$$$\mathrm{find}\:\mathrm{local}\:\mathrm{extrem} \\ $$

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