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Question Number 65398 Answers: 0 Comments: 1

1) calculate A_n =∫∫_([1,n[^2 ) sin(x^2 +3y^2 ) e^(−x^2 −3y^2 ) dxdy 2) determine lim_(n→+∞) A_n

$$\left.\mathrm{1}\right)\:{calculate}\:\:{A}_{{n}} =\int\int_{\left[\mathrm{1},{n}\left[^{\mathrm{2}} \right.\right.} \:\:\:\:\:{sin}\left({x}^{\mathrm{2}} \:+\mathrm{3}{y}^{\mathrm{2}} \right)\:{e}^{−{x}^{\mathrm{2}} −\mathrm{3}{y}^{\mathrm{2}} } {dxdy} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$

Question Number 65399 Answers: 0 Comments: 1

1) calculate A_n = ∫∫_([0,n[^2 ) ((dxdy)/(√(x^2 +y^2 +4))) 2)find lim_(n→+∞) A_n

$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} =\:\int\int_{\left[\mathrm{0},{n}\left[^{\mathrm{2}} \right.\right.} \:\:\:\frac{{dxdy}}{\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{4}}} \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$

Question Number 65407 Answers: 0 Comments: 1

Question Number 65405 Answers: 0 Comments: 1

Question Number 65395 Answers: 1 Comments: 1

Question Number 65383 Answers: 0 Comments: 1

1) calculate ∫_0 ^∞ (dx/(1+e^(nx) )) with n integr natural and n≥1 2) conclude the value of Σ_(k=1) ^∞ (((−1)^(k−1) )/k)

$$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\mathrm{1}+{e}^{{nx}} }\:\:\:{with}\:{n}\:{integr}\:{natural}\:\:{and}\:{n}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{conclude}\:{the}\:{value}\:{of}\:\sum_{{k}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{k}−\mathrm{1}} }{{k}} \\ $$

Question Number 65380 Answers: 1 Comments: 1

Question Number 65387 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((arctan(2x)−arctanx)/x)dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left(\mathrm{2}{x}\right)−{arctanx}}{{x}}{dx} \\ $$

Question Number 65386 Answers: 0 Comments: 1

calculate Σ_(k=1) ^∞ (((−1)^(k−1) )/(99k−1))

$${calculate}\:\sum_{{k}=\mathrm{1}} ^{\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{k}−\mathrm{1}} }{\mathrm{99}{k}−\mathrm{1}} \\ $$

Question Number 65372 Answers: 0 Comments: 4

I=∫_1 ^e (dx/(x(1+ln^2 x)))

$${I}=\int_{\mathrm{1}} ^{{e}} \:\frac{{dx}}{{x}\left(\mathrm{1}+{ln}^{\mathrm{2}} {x}\right)} \\ $$

Question Number 65367 Answers: 2 Comments: 1

Question Number 65366 Answers: 2 Comments: 2

Question Number 65365 Answers: 2 Comments: 0

3sinA+4cosB=6 3cosA+4sinB=1 find angle C

$$\mathrm{3sinA}+\mathrm{4cosB}=\mathrm{6} \\ $$$$\mathrm{3cosA}+\mathrm{4sinB}=\mathrm{1} \\ $$$$\mathrm{find}\:\mathrm{angle}\:\mathrm{C} \\ $$

Question Number 65359 Answers: 0 Comments: 0

φφ

$$\phi\phi \\ $$

Question Number 65356 Answers: 1 Comments: 1

Question Number 65355 Answers: 2 Comments: 1

find ∫ (dx/(√((x+1)(x+2)(x+3))))

$${find}\:\int\:\:\:\frac{{dx}}{\sqrt{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)}} \\ $$

Question Number 65354 Answers: 0 Comments: 3

find ∫ (dx/(√(x^2 +x−2)))

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

Question Number 65352 Answers: 0 Comments: 1

give the integralA_n = ∫_1 ^(+∞) (dt/(1+x^n )) with n integr and n≥2 at form of serie.

$${give}\:{the}\:{integralA}_{{n}} =\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{dt}}{\mathrm{1}+{x}^{{n}} }\:\:{with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{2} \\ $$$${at}\:{form}\:{of}\:{serie}. \\ $$

Question Number 65347 Answers: 1 Comments: 0

Question Number 65345 Answers: 1 Comments: 4

find the maximum value of sin^(2018) x +cos^(2019) x ?

$$\mathrm{find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{sin}^{\mathrm{2018}} \mathrm{x}\:+\mathrm{cos}^{\mathrm{2019}} \mathrm{x}\:? \\ $$

Question Number 65335 Answers: 0 Comments: 0

Question Number 65334 Answers: 1 Comments: 0

Question Number 65332 Answers: 0 Comments: 1

Question Number 65333 Answers: 1 Comments: 1

Question Number 65314 Answers: 0 Comments: 1

Question Number 65312 Answers: 0 Comments: 2

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