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Question Number 84574    Answers: 0   Comments: 1

calculate I_n =∫_0 ^1 sin(narcsinx)dx

$${calculate}\:\:{I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:{sin}\left({narcsinx}\right){dx} \\ $$

Question Number 84572    Answers: 0   Comments: 0

let F(z) =(z^2 /(1+z^7 )) 1) factorize inside C[x] and R[x] z^7 +1 2) decompose inside C(x)and R(x) the fraction F(x)

$${let}\:\:{F}\left({z}\right)\:=\frac{{z}^{\mathrm{2}} }{\mathrm{1}+{z}^{\mathrm{7}} } \\ $$$$\left.\mathrm{1}\right)\:{factorize}\:{inside}\:{C}\left[{x}\right]\:{and}\:{R}\left[{x}\right] \\ $$$${z}^{\mathrm{7}} \:+\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{decompose}\:{inside}\:{C}\left({x}\right){and}\:{R}\left({x}\right) \\ $$$${the}\:{fraction}\:{F}\left({x}\right) \\ $$

Question Number 84571    Answers: 0   Comments: 0

calculate S_n =Σ_(k=1) ^n (((−1)^k )/(√k))

$${calculate}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{{k}} }{\sqrt{{k}}} \\ $$

Question Number 84570    Answers: 1   Comments: 1

calculate ∫_1 ^(+∞) ((arctan((3/x)))/x^2 )dx

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

Question Number 84569    Answers: 1   Comments: 0

find ∫ (dx/(1+tan^4 x))

$${find}\:\:\int\:\:\:\:\frac{{dx}}{\mathrm{1}+{tan}^{\mathrm{4}} {x}} \\ $$

Question Number 84568    Answers: 0   Comments: 4

without L′hopital lim_(x→−(1/2)) ((2x^3 +3x^2 −(√(a+bx)))/(4x^2 −1)) = −(3/4) find a+b

$$\mathrm{without}\:\mathrm{L}'\mathrm{hopital} \\ $$$$\underset{{x}\rightarrow−\frac{\mathrm{1}}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\mathrm{2x}^{\mathrm{3}} +\mathrm{3x}^{\mathrm{2}} −\sqrt{\mathrm{a}+\mathrm{bx}}}{\mathrm{4x}^{\mathrm{2}} −\mathrm{1}}\:=\:−\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\mathrm{find}\:\mathrm{a}+\mathrm{b} \\ $$

Question Number 84566    Answers: 0   Comments: 0

Question Number 84564    Answers: 0   Comments: 1

find arg(z) given that z = ((1 + i)/(1−i))

$$\mathrm{find}\:\mathrm{arg}\left(\mathrm{z}\right)\:\mathrm{given}\:\mathrm{that}\:\:\mathrm{z}\:=\:\frac{\mathrm{1}\:+\:{i}}{\mathrm{1}−{i}} \\ $$

Question Number 84561    Answers: 1   Comments: 0

∫_0 ^∞ ∫_0 ^∞ ((cos(x−y)−cos(x))/(xy))dx dy

$$\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \frac{{cos}\left({x}−{y}\right)−{cos}\left({x}\right)}{{xy}}{dx}\:{dy} \\ $$

Question Number 84558    Answers: 0   Comments: 1

happy π day

$${happy}\:\pi\:{day} \\ $$

Question Number 84557    Answers: 0   Comments: 1

Question Number 84556    Answers: 1   Comments: 1

∫ sin^(−1) (((2x+2)/(√(4x^2 +8x+13)))) dx

$$\int\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{2x}+\mathrm{2}}{\sqrt{\mathrm{4x}^{\mathrm{2}} +\mathrm{8x}+\mathrm{13}}}\right)\:\mathrm{dx} \\ $$

Question Number 84553    Answers: 0   Comments: 3

Find mininum value of n such that both n + 3 and 2020n + 1 are square numbers .

$${Find}\:\:{mininum}\:\:{value}\:\:{of}\:\:{n}\:\:{such}\:\:{that} \\ $$$${both}\:\:{n}\:+\:\mathrm{3}\:\:\:{and}\:\:\mathrm{2020}{n}\:+\:\mathrm{1}\:\:{are}\:\:{square}\:\:{numbers}\:. \\ $$

Question Number 84549    Answers: 1   Comments: 0

Question Number 84544    Answers: 0   Comments: 0

solve xy^(′′) =y^′ (e^y −1)

$${solve}\: \\ $$$${xy}^{''} ={y}^{'} \left({e}^{{y}} −\mathrm{1}\right) \\ $$

Question Number 84543    Answers: 0   Comments: 3

Determine the value of a,b ,c so that _(x→0) ^(lim) (((a +b cos x) x−c sin x)/x^5 )=1

$$\boldsymbol{\mathrm{Determine}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\:,\boldsymbol{\mathrm{c}}\:\:\boldsymbol{\mathrm{so}}\:\boldsymbol{\mathrm{that}} \\ $$$$\:\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\overset{\mathrm{lim}} {\:}}\:\frac{\left(\boldsymbol{\mathrm{a}}\:+\boldsymbol{\mathrm{b}}\:\mathrm{cos}\:\mathrm{x}\right)\:\mathrm{x}−\boldsymbol{\mathrm{c}}\:\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{5}} }=\mathrm{1} \\ $$

Question Number 84532    Answers: 1   Comments: 1

x> 0 , y > 0 prove that ((xy)/(x+y)) < x

$$\mathrm{x}>\:\mathrm{0}\:,\:\mathrm{y}\:>\:\mathrm{0}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{xy}}{\mathrm{x}+\mathrm{y}}\:<\:\mathrm{x} \\ $$

Question Number 84531    Answers: 1   Comments: 2

find for equation of image ellipse (x^2 /9) + (y^2 /8) = 1 if reflected with line x + y = −4

$$\mathrm{find}\:\mathrm{for}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{image}\:\mathrm{ellipse} \\ $$$$\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{9}}\:+\:\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{8}}\:=\:\mathrm{1}\:\mathrm{if}\:\mathrm{reflected}\:\mathrm{with}\:\mathrm{line} \\ $$$$\mathrm{x}\:+\:\mathrm{y}\:=\:−\mathrm{4} \\ $$

Question Number 84528    Answers: 0   Comments: 3

1=2

$$\mathrm{1}=\mathrm{2} \\ $$

Question Number 84515    Answers: 1   Comments: 0

Q.solve x^3 −x=x!

$${Q}.{solve} \\ $$$${x}^{\mathrm{3}} −{x}={x}! \\ $$

Question Number 84512    Answers: 1   Comments: 0

Question Number 84510    Answers: 2   Comments: 0

Question Number 84505    Answers: 0   Comments: 1

2)calculate I(ξ) =∫_ξ ^1 (dx/(√(1+ξx^2 −(√(1−ξx^2 ))))) 1)find lim_(ξ→0) I(ξ)

$$\left.\mathrm{2}\right){calculate}\:\:\:{I}\left(\xi\right)\:=\int_{\xi} ^{\mathrm{1}} \:\:\:\:\:\:\frac{{dx}}{\sqrt{\mathrm{1}+\xi{x}^{\mathrm{2}} −\sqrt{\mathrm{1}−\xi{x}^{\mathrm{2}} }}} \\ $$$$\left.\mathrm{1}\right){find}\:{lim}_{\xi\rightarrow\mathrm{0}} \:\:{I}\left(\xi\right) \\ $$

Question Number 84498    Answers: 0   Comments: 1

∫(√x) cos(√x) dx

$$\int\sqrt{{x}}\:{cos}\sqrt{{x}}\:{dx} \\ $$

Question Number 84497    Answers: 0   Comments: 1

∫(x^2 /(1+x^5 )) dx

$$\int\frac{{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{5}} }\:{dx} \\ $$$$ \\ $$

Question Number 84496    Answers: 1   Comments: 1

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