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Question Number 68596 Answers: 0 Comments: 1

calculate ∫_(π/2) ^(π/3) ((xdx)/(3+cosx))

$${calculate}\:\int_{\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{3}}} \:\:\:\:\frac{{xdx}}{\mathrm{3}+{cosx}} \\ $$

Question Number 68595 Answers: 0 Comments: 1

calculate A_λ =∫_0 ^∞ (e^(−λx^2 ) /(x^4 +1))dx with λ>0 and find ∫_0 ^1 A_λ dλ

$${calculate}\:\:{A}_{\lambda} =\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{e}^{−\lambda{x}^{\mathrm{2}} } }{{x}^{\mathrm{4}} +\mathrm{1}}{dx}\:\:{with}\:\lambda>\mathrm{0}\:\:{and}\: \\ $$$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{A}_{\lambda} \:{d}\lambda \\ $$

Question Number 68594 Answers: 0 Comments: 0

calculate ∫_0 ^(2π) (dx/(cosx +sin(2x)))

$${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{dx}}{{cosx}\:+{sin}\left(\mathrm{2}{x}\right)} \\ $$

Question Number 68593 Answers: 0 Comments: 1

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

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

Question Number 68592 Answers: 0 Comments: 2

find Σ_(n=1) ^∞ (1/(n^2 (n+1)^3 ))

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

Question Number 68591 Answers: 0 Comments: 6

Question Number 68589 Answers: 1 Comments: 0

Question Number 68632 Answers: 0 Comments: 0

(sin(π/9) + i sin((3π)/(18)))^(−9)

$$\left({sin}\frac{\pi}{\mathrm{9}}\:+\:{i}\:{sin}\frac{\mathrm{3}\pi}{\mathrm{18}}\right)^{−\mathrm{9}} \\ $$

Question Number 68554 Answers: 0 Comments: 4

Question Number 68549 Answers: 1 Comments: 3

y=(x^3 /(x^2 +1)) y^(−1) =...

$${y}=\frac{{x}^{\mathrm{3}} }{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$${y}^{−\mathrm{1}} =... \\ $$

Question Number 68546 Answers: 1 Comments: 0

find the range and domain of f(x) f(x)=(√(sin^(−1) (ln(x/(10)))))

$${find}\:{the}\:{range}\:{and}\:{domain}\:{of}\:{f}\left({x}\right) \\ $$$$ \\ $$$${f}\left({x}\right)=\sqrt{{sin}^{−\mathrm{1}} \left({ln}\frac{{x}}{\mathrm{10}}\right)} \\ $$

Question Number 68541 Answers: 1 Comments: 1

Question Number 68537 Answers: 2 Comments: 0

Question Number 68532 Answers: 0 Comments: 0

Question Number 68521 Answers: 0 Comments: 1

lim_(x→0) ((4 sin x + 2 tan x − 6x)/x^5 ) = ? Without L′Hospital

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{4}\:\mathrm{sin}\:{x}\:+\:\mathrm{2}\:\mathrm{tan}\:{x}\:−\:\mathrm{6}{x}}{{x}^{\mathrm{5}} }\:\:=\:\:? \\ $$$${Without}\:\:{L}'{Hospital} \\ $$

Question Number 68517 Answers: 0 Comments: 0

Question Number 68515 Answers: 1 Comments: 2

Question Number 68510 Answers: 1 Comments: 0

Question Number 68509 Answers: 0 Comments: 0

Question Number 68508 Answers: 0 Comments: 0

Question Number 68506 Answers: 0 Comments: 0

y′=4y^2 +x^2 +1 what the primitive solution

$${y}'=\mathrm{4}{y}^{\mathrm{2}} +{x}^{\mathrm{2}} +\mathrm{1} \\ $$$${what}\:{the}\:{primitive}\:{solution} \\ $$

Question Number 68503 Answers: 0 Comments: 8

Question Number 68524 Answers: 1 Comments: 0

Question Number 68528 Answers: 0 Comments: 0

lim_(t→∞) [(1/t) ∫_1 ^( t) (t)^(1/x) dx]

$$\underset{{t}\rightarrow\infty} {\mathrm{lim}}\:\left[\frac{\mathrm{1}}{{t}}\:\int_{\mathrm{1}} ^{\:{t}} \:\sqrt[{{x}}]{{t}}\:{dx}\right] \\ $$

Question Number 68495 Answers: 1 Comments: 1

Whats is the value of sin (6°)?

$$\mathrm{Whats}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{sin}\:\left(\mathrm{6}°\right)? \\ $$

Question Number 68493 Answers: 1 Comments: 0

My question is about the analogical axiams of the foundation geometry in mathematocs. As it Is a well knowen axum in geometry starts from the sefinition of a point which gives gives the path analogically to line, plane, and solids. Know my truoble comes at these axiumes areise from not ne being they are aziyma ^ but the analogu effect at giving the definatiom of the solid} 1−Apoimt is a dimenstin less. mathematixal abstruct. 2− a line is the collextom of points which has only one dimension. 3− a plane is the collection of lines which have onlu?two dimensions 3−a solid is the collwxripm of plans which has three dimensions. Now the first three definationa arsties are mathe are mathematical ideasor abstruct while the last mathematical abstruct is real. ow on earth a real object is formed from the collextion of unreal planes

$${My}\:{question}\:{is}\:{about}\:{the}\:{analogical} \\ $$$${axiams}\:{of}\:{the}\:{foundation}\:{geometry}\:{in} \\ $$$${mathematocs}. \\ $$$${As}\:{it}\:{Is}\:\:{a}\:{well}\:{knowen}\:{axum}\:{in}\:\:{geometry} \\ $$$${starts}\:{from}\:{the}\:{sefinition}\:{of}\:{a}\:{point}\:{which}\:{gives} \\ $$$${gives}\:{the}\:{path}\:{analogically}\:\:{to}\:{line},\:{plane},\:{and}\: \\ $$$${solids}. \\ $$$${Know}\:{my}\:{truoble}\:\:{comes}\:{at}\:{these} \\ $$$${axiumes}\:{areise}\:{from}\:{not}\:{ne}\:{being}\:{they} \\ $$$${are}\:{aziyma}\bar {\:}{but}\:{the}\:{analogu}\:{effect}\:{at} \\ $$$$\left.{giving}\:{the}\:{definatiom}\:{of}\:{the}\:{solid}\right\} \\ $$$$\mathrm{1}−{Apoimt}\:{is}\:{a}\:{dimenstin}\:{less}. \\ $$$$\:{mathematixal}\:{abstruct}. \\ $$$$\mathrm{2}−\:{a}\:{line}\:{is}\:{the}\:{collextom}\:{of}\:{points} \\ $$$$\:\:{which}\:{has}\:{only}\:{one}\:{dimension}. \\ $$$$\mathrm{3}−\:{a}\:{plane}\:{is}\:{the}\:{collection}\:\:{of}\:{lines}\: \\ $$$${which}\:{have}\:{onlu}?{two}\:{dimensions}\: \\ $$$$\mathrm{3}−{a}\:\:{solid}\:{is}\:{the}\:{collwxripm}\:{of}\:{plans} \\ $$$${which}\:{has}\:{three}\:{dimensions}. \\ $$$$ \\ $$$$\:\:\:\:\:\:{Now}\:{the}\:{first}\:{three}\:{definationa}\:{arsties}\:{are}\:{mathe} \\ $$$${are}\:{mathematical}\:{ideasor}\:{abstruct} \\ $$$${while}\:{the}\:{last}\:{mathematical}\:{abstruct}\:{is}\:{real}. \\ $$$${ow}\:{on}\:{earth}\:{a}\:{real}\:{object}\:{is}\:{formed} \\ $$$${from}\:{the}\:{collextion}\:{of}\:{unreal}\:{planes} \\ $$

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