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AllQuestion and Answers: Page 1456

Question Number 64941 Answers: 0 Comments: 0

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Question Number 64916 Answers: 1 Comments: 6

Question Number 64909 Answers: 1 Comments: 2

Question Number 64905 Answers: 0 Comments: 0

∫log (tan x)dx

$$\int\mathrm{log}\:\left(\mathrm{tan}\:\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 64904 Answers: 0 Comments: 2

calculate ∫_1 ^2 ∫_0 ^x (1/((x^2 +y^2 )^(3/2) ))dydx

$${calculate}\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\int_{\mathrm{0}} ^{{x}} \:\:\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} }{dydx}\: \\ $$

Question Number 64903 Answers: 1 Comments: 2

1, 3, 7, 15, 30, 57, 103, x What′s x ?

$$\mathrm{1},\:\mathrm{3},\:\mathrm{7},\:\mathrm{15},\:\mathrm{30},\:\mathrm{57},\:\mathrm{103},\:{x} \\ $$$${What}'{s}\:\:{x}\:? \\ $$

Question Number 64901 Answers: 1 Comments: 11

Question Number 64895 Answers: 0 Comments: 0

Question Number 64894 Answers: 0 Comments: 0

Question Number 64893 Answers: 0 Comments: 0

Question Number 64892 Answers: 0 Comments: 0

Question Number 64887 Answers: 1 Comments: 0

Question Number 64886 Answers: 0 Comments: 0

let f(x) =cos((1/x)) 1) calculate f^((n)) (x) 2) developp f at integr serie at x_0 =(3/π)

$${let}\:{f}\left({x}\right)\:={cos}\left(\frac{\mathrm{1}}{{x}}\right)\:\:\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:{at}\:{x}_{\mathrm{0}} =\frac{\mathrm{3}}{\pi} \\ $$

Question Number 64867 Answers: 1 Comments: 0

x^4 +(2i−3)x^3 −(1+6i)x^2 +(3−2i)x−2=0

$${x}^{\mathrm{4}} +\left(\mathrm{2}{i}−\mathrm{3}\right){x}^{\mathrm{3}} −\left(\mathrm{1}+\mathrm{6}{i}\right){x}^{\mathrm{2}} +\left(\mathrm{3}−\mathrm{2}{i}\right){x}−\mathrm{2}=\mathrm{0} \\ $$

Question Number 64866 Answers: 0 Comments: 3

find ∫_1 ^(+∞) (dx/(x^2 (√(1+x+x^2 ))))

$${find}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{dx}}{{x}^{\mathrm{2}} \sqrt{\mathrm{1}+{x}+{x}^{\mathrm{2}} }} \\ $$

Question Number 64860 Answers: 0 Comments: 6

Question Number 64857 Answers: 0 Comments: 3

Question Number 64853 Answers: 1 Comments: 0

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Question Number 64851 Answers: 0 Comments: 6

Find all solutions of x real numbers f^(−1) (x) = f(x)

$${Find}\:\:{all}\:\:{solutions}\:\:{of}\:\:{x}\:\:{real}\:\:{numbers}\: \\ $$$$\:\:\:\:\:\:\:\:{f}\:^{−\mathrm{1}} \left({x}\right)\:\:=\:\:{f}\left({x}\right) \\ $$

Question Number 64850 Answers: 0 Comments: 4

let A_λ =∫_0 ^π (dx/(λ +cosx +sinx)) (λ ∈ R) 1) find a explicit form of A_λ 2) find also B_λ =∫_0 ^π (dx/((λ +cosx +sinx)^2 )) 3) calculate ∫_0 ^π (dx/(2+cosx +sinx)) and ∫_0 ^π (dx/((3+cosx +sinx)^2 ))

$${let}\:{A}_{\lambda} \:=\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{dx}}{\lambda\:\:+{cosx}\:+{sinx}}\:\:\:\:\left(\lambda\:\in\:{R}\right) \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{A}_{\lambda} \\ $$$$\left.\mathrm{2}\right)\:\:{find}\:{also}\:{B}_{\lambda} \:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dx}}{\left(\lambda\:+{cosx}\:+{sinx}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{dx}}{\mathrm{2}+{cosx}\:+{sinx}}\:\:{and}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dx}}{\left(\mathrm{3}+{cosx}\:+{sinx}\right)^{\mathrm{2}} } \\ $$

Question Number 64829 Answers: 2 Comments: 4

Question Number 64837 Answers: 1 Comments: 0

{ ((x^(√y) + y^(√x) = ((49)/(48)))),(((√x) + (√y) = (7/2))) :} find x and y

$$\begin{cases}{{x}^{\sqrt{{y}}} \:+\:{y}^{\sqrt{{x}}} \:=\:\frac{\mathrm{49}}{\mathrm{48}}}\\{\sqrt{{x}}\:+\:\sqrt{{y}}\:=\:\frac{\mathrm{7}}{\mathrm{2}}}\end{cases} \\ $$$$ \\ $$$${find}\:{x}\:{and}\:{y} \\ $$$$ \\ $$

Question Number 64824 Answers: 0 Comments: 0

Question Number 64823 Answers: 0 Comments: 5

Question Number 64820 Answers: 0 Comments: 1

calculate Σ_(n=1) ^∞ (((−1)^n )/(n^2 (n+1)(n+2)))

$${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)} \\ $$

Question Number 64819 Answers: 0 Comments: 2

calculate Σ_(n=1) ^∞ (((2n+1)(−1)^n )/(n^3 (n+1)^2 ))

$${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\left(\mathrm{2}{n}+\mathrm{1}\right)\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{3}} \left({n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

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