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AllQuestion and Answers: Page 1704

Question Number 35294 Answers: 1 Comments: 1

Question Number 35291 Answers: 1 Comments: 1

solve in Z x^3 +6y^3 =4z^3

$${solve}\:\:{in}\:{Z}\:\:{x}^{\mathrm{3}} +\mathrm{6}{y}^{\mathrm{3}} =\mathrm{4}{z}^{\mathrm{3}} \\ $$

Question Number 35290 Answers: 0 Comments: 1

∫((x+1)/x^3 )dx

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

Question Number 35319 Answers: 2 Comments: 0

Question Number 35267 Answers: 1 Comments: 0

Question Number 35265 Answers: 0 Comments: 0

4−4×4+4=

$$\mathrm{4}−\mathrm{4}×\mathrm{4}+\mathrm{4}= \\ $$

Question Number 35279 Answers: 0 Comments: 3

Question Number 35256 Answers: 1 Comments: 1

Factorize :x^5 −y^5

$$\mathrm{Factorize}\::\mathrm{x}^{\mathrm{5}} −\mathrm{y}^{\mathrm{5}} \\ $$

Question Number 35248 Answers: 0 Comments: 1

Question Number 35246 Answers: 1 Comments: 1

if x^p + y^q =(x + y)^(p+q) prove that (dy/dx)=(y/x)

$${if}\:{x}^{{p}} \:+\:{y}^{{q}} \:=\left({x}\:+\:{y}\right)^{{p}+{q}} \: \\ $$$${prove}\:{that}\:\frac{{dy}}{{dx}}=\frac{{y}}{{x}} \\ $$

Question Number 35245 Answers: 0 Comments: 7

express ((7x+4)/(x^3 +x^2 + 9x +9)) in partial fraction

$${express}\:\frac{\mathrm{7}{x}+\mathrm{4}}{{x}^{\mathrm{3}} \:+{x}^{\mathrm{2}} +\:\mathrm{9}{x}\:+\mathrm{9}}\:{in}\:{partial} \\ $$$${fraction} \\ $$

Question Number 35244 Answers: 0 Comments: 1

if y=((sin^(−1) x)/(1−x^2 )) show that (1−x^2 )(dy/dx) −xy=1

$${if}\:\:{y}=\frac{{sin}^{−\mathrm{1}} {x}}{\mathrm{1}−{x}^{\mathrm{2}} }\:\:{show}\:{that}\: \\ $$$$\left(\mathrm{1}−{x}^{\mathrm{2}} \right)\frac{{dy}}{{dx}}\:−{xy}=\mathrm{1} \\ $$

Question Number 35242 Answers: 1 Comments: 1

find ∫_0 ^π ((xdx)/(1+sinx))

$${find}\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{xdx}}{\mathrm{1}+{sinx}} \\ $$

Question Number 35241 Answers: 2 Comments: 6

calculate ∫_0 ^π ((x dx)/(3 +cosx)) .

$${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{x}\:{dx}}{\mathrm{3}\:+{cosx}}\:\:. \\ $$

Question Number 35238 Answers: 0 Comments: 1

study the convergence of ∫_1 ^(+∞) ((e^(−3x) −e^(−2x) )/x^2 )dx

$${study}\:{the}\:{convergence}\:{of} \\ $$$$\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{e}^{−\mathrm{3}{x}} \:−{e}^{−\mathrm{2}{x}} }{{x}^{\mathrm{2}} }{dx}\: \\ $$

Question Number 35237 Answers: 0 Comments: 1

study the convergence of ∫_0 ^∞ ((e^(−x) −e^(−x^2 ) )/x)dx .

$${study}\:{the}\:{convergence}\:{of} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{x}} \:−{e}^{−{x}^{\mathrm{2}} } }{{x}}{dx}\:. \\ $$

Question Number 35236 Answers: 0 Comments: 0

letf(x)=arctan(1+ix) with ∣x∣<1 developp f at integr serie.

$${letf}\left({x}\right)={arctan}\left(\mathrm{1}+{ix}\right)\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$${developp}\:{f}\:\:{at}\:{integr}\:{serie}. \\ $$

Question Number 35235 Answers: 0 Comments: 2

let f(x)= e^(−2x) arctanx 1) calculate f^((n)) (x) 2) find f^((n)) (0) 3) developp f at integr serie

$${let}\:{f}\left({x}\right)=\:{e}^{−\mathrm{2}{x}} \:{arctanx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$

Question Number 35234 Answers: 0 Comments: 1

let f(x) =e^(−x^n ) with n fromN developp f at integr serie .

$${let}\:{f}\left({x}\right)\:={e}^{−{x}^{{n}} } \:\:\:\:\:{with}\:{n}\:{fromN} \\ $$$${developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$

Question Number 35232 Answers: 0 Comments: 0

what is the value of cos z and sinz if z=re^(iθ) r>0 ?

$${what}\:{is}\:{the}\:{value}\:{of}\:{cos}\:{z}\:{and}\:{sinz} \\ $$$${if}\:{z}={re}^{{i}\theta} \:\:\:\:{r}>\mathrm{0}\:\:? \\ $$

Question Number 35231 Answers: 0 Comments: 1

what is the value of cos(1+i) and cos(1−i)?

$${what}\:{is}\:{the}\:{value}\:{of}\:{cos}\left(\mathrm{1}+{i}\right)\:{and} \\ $$$${cos}\left(\mathrm{1}−{i}\right)? \\ $$

Question Number 35229 Answers: 1 Comments: 2

find the value of integral ∫_0 ^∞ e^(−(2+ia)^2 t^2 ) dt with a from R ∣a∣<1.

$${find}\:{the}\:{value}\:{of}\:{integral} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\left(\mathrm{2}+{ia}\right)^{\mathrm{2}} {t}^{\mathrm{2}} } {dt}\:\:\:\:{with}\:{a}\:{from}\:{R}\:\:\:\:\mid{a}\mid<\mathrm{1}. \\ $$

Question Number 35228 Answers: 0 Comments: 2

find the value of integral ∫_0 ^∞ e^(−px) ((sin(qx))/(√x))dx with p>0 and q>0

$${find}\:{the}\:{value}\:{of}\:{integral} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{px}} \:\:\:\frac{{sin}\left({qx}\right)}{\sqrt{{x}}}{dx}\:\:{with}\:{p}>\mathrm{0}\:{and}\:{q}>\mathrm{0} \\ $$

Question Number 35226 Answers: 0 Comments: 4

1) calculate f(a) = ∫_0 ^π (dx/(a sin^2 x +cos^2 x)) with a>0 2) find the value of g(a) = ∫_0 ^π ((sin^2 x)/((a sin^2 x +cos^2 x)^2 ))dx

$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\:\:\:\frac{{dx}}{{a}\:{sin}^{\mathrm{2}} {x}\:\:+{cos}^{\mathrm{2}} {x}} \\ $$$${with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:{g}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{sin}^{\mathrm{2}} {x}}{\left({a}\:{sin}^{\mathrm{2}} {x}\:+{cos}^{\mathrm{2}} {x}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 35225 Answers: 0 Comments: 4

1) find f(a) = ∫_0 ^(2π) (dt/(a cos^2 t + sin^2 t)) with a≠0 2) find g(a) = ∫_0 ^(2π) ((cos^2 t)/((a cos^2 t +sin^2 t)^2 ))dt

$$\left.\mathrm{1}\right)\:{find}\:{f}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\:\:\frac{{dt}}{{a}\:{cos}^{\mathrm{2}} {t}\:+\:{sin}^{\mathrm{2}} {t}}\:{with}\:{a}\neq\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{g}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{cos}^{\mathrm{2}} {t}}{\left({a}\:{cos}^{\mathrm{2}} {t}\:+{sin}^{\mathrm{2}} {t}\right)^{\mathrm{2}} }{dt}\: \\ $$

Question Number 35224 Answers: 1 Comments: 0

calculate ∫_0 ^(2π) ((1+2cost)/(5+4cost))dt

$${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\:\frac{\mathrm{1}+\mathrm{2}{cost}}{\mathrm{5}+\mathrm{4}{cost}}{dt} \\ $$

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