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Question Number 32501    Answers: 1   Comments: 0

(x−2y+3)^2 +(3x+4y−1)^2 =100 what is the area of the ellipse?

$$\left(\mathrm{x}−\mathrm{2y}+\mathrm{3}\right)^{\mathrm{2}} +\left(\mathrm{3x}+\mathrm{4y}−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{100} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ellipse}? \\ $$

Question Number 32500    Answers: 1   Comments: 0

proof: (−a)(−b)=ab

$${proof}:\:\left(−{a}\right)\left(−{b}\right)={ab} \\ $$

Question Number 32499    Answers: 2   Comments: 0

proof: a(−b)=(−a)b=−(ab)

$${proof}:\:{a}\left(−{b}\right)=\left(−{a}\right){b}=−\left({ab}\right) \\ $$

Question Number 32496    Answers: 0   Comments: 0

Question Number 32495    Answers: 0   Comments: 0

Question Number 32494    Answers: 0   Comments: 0

Question Number 32493    Answers: 0   Comments: 0

Question Number 32490    Answers: 1   Comments: 0

if f(x)=∣x∣ and g(x)=2x−3.Find the domain of gof

$${if}\:{f}\left({x}\right)=\mid{x}\mid\:{and}\:{g}\left({x}\right)=\mathrm{2}{x}−\mathrm{3}.{Find} \\ $$$${the}\:{domain}\:{of}\:{gof} \\ $$

Question Number 32489    Answers: 1   Comments: 1

find the range of f(x)=1+(√(2x−1))

$${find}\:{the}\:{range}\:{of}\:{f}\left({x}\right)=\mathrm{1}+\sqrt{\mathrm{2}{x}−\mathrm{1}} \\ $$

Question Number 32487    Answers: 0   Comments: 0

let x>1 and ξ(x) =Σ_(n=1) ^∞ (1/n^x ) (zeta function of Rieman) 1) calculate lim_(x→+∞) ξ(x) 2)let consider s(x)=Σ_(n=2) ^∞ ((ξ(n))/n) x^n study the convergence of s(x) and find a simple form of s(x).

$${let}\:{x}>\mathrm{1}\:{and}\:\xi\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}^{{x}} }\:\left({zeta}\:{function}\:{of}\:{Rieman}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{x}\rightarrow+\infty} \xi\left({x}\right) \\ $$$$\left.\mathrm{2}\right){let}\:{consider}\:\:{s}\left({x}\right)=\sum_{{n}=\mathrm{2}} ^{\infty} \:\:\frac{\xi\left({n}\right)}{{n}}\:{x}^{{n}} \:{study}\:{the}\:{convergence} \\ $$$${of}\:{s}\left({x}\right)\:{and}\:{find}\:{a}\:{simple}\:{form}\:{of}\:{s}\left({x}\right). \\ $$

Question Number 32486    Answers: 0   Comments: 1

find lim_(n→∞) Σ_(k=n+1) ^(2n) sin((1/k)).

$${find}\:{lim}_{{n}\rightarrow\infty} \:\:\:\sum_{{k}={n}+\mathrm{1}} ^{\mathrm{2}{n}} \:{sin}\left(\frac{\mathrm{1}}{{k}}\right). \\ $$

Question Number 32485    Answers: 0   Comments: 1

let give α>1 find lim_(n→∞) Σ_(k=n+1) ^(2n) (1/k^α ) .

$${let}\:{give}\:\alpha>\mathrm{1}\:{find}\:{lim}_{{n}\rightarrow\infty} \:\:\sum_{{k}={n}+\mathrm{1}} ^{\mathrm{2}{n}} \:\:\frac{\mathrm{1}}{{k}^{\alpha} }\:. \\ $$

Question Number 32484    Answers: 0   Comments: 2

∫_1 ^2 ∫_0 ^1 ((ln(x+y))/((x+y))) dx dy

$$ \\ $$$$\int_{\mathrm{1}} ^{\mathrm{2}} \int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left({x}+{y}\right)}{\left({x}+{y}\right)}\:{dx}\:{dy} \\ $$

Question Number 32483    Answers: 0   Comments: 2

calculate ∫_0 ^(2π) (dx/(1+2cosx)) .

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\:\frac{{dx}}{\mathrm{1}+\mathrm{2}{cosx}}\:. \\ $$

Question Number 32482    Answers: 0   Comments: 0

find f(x)= ∫_0 ^π ((sin^2 t)/(1−2xcost +x^2 ))dt with ∣x∣<1 .

$${find}\:\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\:\frac{{sin}^{\mathrm{2}} {t}}{\mathrm{1}−\mathrm{2}{xcost}\:+{x}^{\mathrm{2}} }{dt}\:{with}\:\mid{x}\mid<\mathrm{1}\:. \\ $$

Question Number 32481    Answers: 0   Comments: 0

find ∫_0 ^∞ ((√(t )) −2(√(t+1)) +(√(t+2))) dt

$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\left(\sqrt{{t}\:}\:−\mathrm{2}\sqrt{{t}+\mathrm{1}}\:+\sqrt{\left.{t}+\mathrm{2}\right)}\:{dt}\right. \\ $$

Question Number 32480    Answers: 0   Comments: 1

find ∫_0 ^α (√(tanx)) dx with 0<α<(π/2) .

$${find}\:\:\int_{\mathrm{0}} ^{\alpha} \:\sqrt{{tanx}}\:{dx}\:{with}\:\mathrm{0}<\alpha<\frac{\pi}{\mathrm{2}}\:. \\ $$

Question Number 32479    Answers: 0   Comments: 0

find ∫_0 ^∞ (dx/((x^2 +1)(x^2 +3x +1)))

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\mathrm{3}{x}\:+\mathrm{1}\right)} \\ $$

Question Number 32478    Answers: 0   Comments: 1

find ∫_0 ^∞ ln(((1+t^2 )/t^2 ))dt

$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:{ln}\left(\frac{\mathrm{1}+{t}^{\mathrm{2}} }{{t}^{\mathrm{2}} }\right){dt} \\ $$

Question Number 32477    Answers: 0   Comments: 1

calcilate ∫_0 ^1 ((ln(1−x^2 ))/x^2 )dx

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

Question Number 32492    Answers: 0   Comments: 0

Question Number 32474    Answers: 0   Comments: 0

Question Number 32473    Answers: 0   Comments: 0

Question Number 32472    Answers: 0   Comments: 0

Question Number 32471    Answers: 0   Comments: 0

Question Number 32470    Answers: 0   Comments: 0

lim_(x→∞) x(sec((1/(√x))) − 1)=...

$$\underset{{x}\rightarrow\infty} {{lim}}\:{x}\left({sec}\left(\frac{\mathrm{1}}{\sqrt{{x}}}\right)\:−\:\mathrm{1}\right)=... \\ $$

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