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Question Number 156178 Answers: 1 Comments: 0

Question Number 156177 Answers: 1 Comments: 0

∫_(−∞) ^∞ ((sin (x))/(x^2 +x+1))dx=?

$$\int_{−\infty} ^{\infty} \frac{\mathrm{sin}\:\left({x}\right)}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}{dx}=? \\ $$

Question Number 156176 Answers: 1 Comments: 0

Question Number 156172 Answers: 3 Comments: 6

Question Number 156170 Answers: 2 Comments: 0

Question Number 156164 Answers: 1 Comments: 0

Question Number 156182 Answers: 1 Comments: 0

Question Number 156152 Answers: 0 Comments: 1

{ ((a+b+c=1)),((a^2 +b^2 +c^2 =2)),((a^3 +b^3 +c^3 =3)) :} a^6 +b^6 +c^6 =?

$$\begin{cases}{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}}=\mathrm{1}}\\{\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{b}}^{\mathrm{2}} +\boldsymbol{\mathrm{c}}^{\mathrm{2}} =\mathrm{2}}\\{\boldsymbol{\mathrm{a}}^{\mathrm{3}} +\boldsymbol{\mathrm{b}}^{\mathrm{3}} +\boldsymbol{\mathrm{c}}^{\mathrm{3}} =\mathrm{3}}\end{cases} \\ $$$$\boldsymbol{\mathrm{a}}^{\mathrm{6}} +\boldsymbol{\mathrm{b}}^{\mathrm{6}} +\boldsymbol{\mathrm{c}}^{\mathrm{6}} =? \\ $$

Question Number 156138 Answers: 0 Comments: 1

la valeur de l′integrale ∫^1 _o x(√(√(√x)))

$${la}\:{valeur}\:{de}\:{l}'{integrale} \\ $$$$\underset{{o}} {\int}^{\mathrm{1}} {x}\sqrt{\sqrt{\sqrt{{x}}}} \\ $$$$ \\ $$

Question Number 156137 Answers: 1 Comments: 0

Question Number 156136 Answers: 1 Comments: 0

soit E(x) la partie entiere ,p<q alors la valeur de ∫^q _p E(x)dx =?

$${soit}\:{E}\left({x}\right)\:{la}\:{partie}\:{entiere}\:,{p}<{q} \\ $$$${alors}\:{la}\:{valeur}\:{de}\: \\ $$$$\underset{{p}} {\int}^{{q}} {E}\left({x}\right){dx}\:=? \\ $$

Question Number 156133 Answers: 1 Comments: 1

Question Number 156128 Answers: 1 Comments: 0

f:X→Y f(E\F)=f(E)\f(F)⇒f is 1 to 1 I think it is not true since let x1 x2 x3∈E ,x3 x4∈F, and f(x1)=f( x2) it will be not true. but my friend say by ∼q⇒∼p f is not 1 to 1 ⇒f(E\F)≠f(E)\f(F),and take x1 x2∈X, f(x1)=f(x2)=y0 E={x1 ,x2} F={x2} and can proof it is true but I do not know which is true how to proof it?

$$\:{f}:{X}\rightarrow{Y} \\ $$$${f}\left({E}\backslash{F}\right)={f}\left({E}\right)\backslash{f}\left({F}\right)\Rightarrow{f}\:{is}\:\mathrm{1}\:{to}\:\mathrm{1} \\ $$$$ \\ $$$${I}\:{think}\:{it}\:{is}\:{not}\:{true}\: \\ $$$${since}\:{let}\:{x}\mathrm{1}\:{x}\mathrm{2}\:{x}\mathrm{3}\in{E}\:,{x}\mathrm{3}\:{x}\mathrm{4}\in{F}, \\ $$$${and}\:{f}\left({x}\mathrm{1}\right)={f}\left(\:{x}\mathrm{2}\right)\:{it}\:{will}\:{be}\:{not}\:{true}. \\ $$$$ \\ $$$${but}\:{my}\:{friend}\:{say}\:{by}\:\sim{q}\Rightarrow\sim{p} \\ $$$$\:{f}\:{is}\:{not}\:\mathrm{1}\:{to}\:\mathrm{1} \\ $$$$\Rightarrow{f}\left({E}\backslash{F}\right)\neq{f}\left({E}\right)\backslash{f}\left({F}\right),{and}\:{take} \\ $$$${x}\mathrm{1}\:{x}\mathrm{2}\in{X},\:{f}\left({x}\mathrm{1}\right)={f}\left({x}\mathrm{2}\right)={y}\mathrm{0} \\ $$$${E}=\left\{{x}\mathrm{1}\:,{x}\mathrm{2}\right\}\:{F}=\left\{{x}\mathrm{2}\right\} \\ $$$${and}\:\:{can}\:{proof}\:{it}\:{is}\:{true} \\ $$$${but}\:{I}\:{do}\:{not}\:{know}\:{which}\:{is}\:{true} \\ $$$${how}\:{to}\:{proof}\:{it}? \\ $$

Question Number 156126 Answers: 1 Comments: 1

cos(π/5)=...? with solution pls

$$\:\:\:\mathrm{cos}\frac{\pi}{\mathrm{5}}=...?\:\:\mathrm{with}\:\mathrm{solution}\:\mathrm{pls} \\ $$

Question Number 156201 Answers: 0 Comments: 1

A=[((x^n ((x^n^2 ((x^n^3 ∙∙∙∙(x^n^n )^(1/n) ))^(1/n) ))^(1/n) ))^(1/n) ]^(1/n)

$$\:\:{A}=\left[\sqrt[{\mathrm{n}}]{\mathrm{x}^{\mathrm{n}} \sqrt[{\mathrm{n}}]{\mathrm{x}^{\mathrm{n}^{\mathrm{2}} } \sqrt[{\mathrm{n}}]{\mathrm{x}^{\mathrm{n}^{\mathrm{3}} } \centerdot\centerdot\centerdot\centerdot\sqrt[{\mathrm{n}}]{\mathrm{x}^{\mathrm{n}^{\mathrm{n}} } }}}}\right]^{\frac{\mathrm{1}}{\mathrm{n}}} \\ $$

Question Number 156123 Answers: 0 Comments: 0

Question Number 156119 Answers: 1 Comments: 2

solve : ((1+2x)/(1+(√(1+2x))))+((1−2x)/(1−(√(1−2x))))=1

$$\mathrm{solve}\:: \\ $$$$\:\frac{\mathrm{1}+\mathrm{2x}}{\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{2x}}}+\frac{\mathrm{1}−\mathrm{2x}}{\mathrm{1}−\sqrt{\mathrm{1}−\mathrm{2x}}}=\mathrm{1} \\ $$$$ \\ $$

Question Number 156109 Answers: 2 Comments: 0

log _5 ((√(x−9)))−log _5 (3x^2 −12)−log _5 ((√(2x−1))) ≤ 0

$$\:\:\mathrm{log}\:_{\mathrm{5}} \left(\sqrt{\mathrm{x}−\mathrm{9}}\right)−\mathrm{log}\:_{\mathrm{5}} \left(\mathrm{3x}^{\mathrm{2}} −\mathrm{12}\right)−\mathrm{log}\:_{\mathrm{5}} \left(\sqrt{\mathrm{2x}−\mathrm{1}}\right)\:\leqslant\:\mathrm{0} \\ $$

Question Number 156108 Answers: 0 Comments: 0

lim_(x→(π/8)) ((1+cot 6x)/(1−sin 4x)) =?

$$\:\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{8}}} {\mathrm{lim}}\:\frac{\mathrm{1}+\mathrm{cot}\:\mathrm{6x}}{\mathrm{1}−\mathrm{sin}\:\mathrm{4x}}\:=? \\ $$

Question Number 156107 Answers: 1 Comments: 1

(1+(1/x))^(x+1) =(1+(1/(2019)))^(2019)

$$\:\:\:\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}+\mathrm{1}} =\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2019}}\right)^{\mathrm{2019}} \\ $$

Question Number 156106 Answers: 0 Comments: 0

Find an equation of the tangen line to the graph of the given equation at the indicated point P 1). xy+16=0 →P(−2,8) 2). y^2 −4x^2 =5→P(−1,3) 3). 2x^3 −x^2 y+y^3 −1=0→P(2,−3) 4). 3y^4 +4x−x^2 sin y−4=0→P(1,0) 5). y^4 +3 y−4x^2 =5x+1→P(1,−2)

$$\mathrm{Find}\:\mathrm{an}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tangen}\:\mathrm{line} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{graph}\:\mathrm{of}\:\mathrm{the}\:\mathrm{given}\:\mathrm{equation}\: \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{indicated}\:\mathrm{point}\:\mathrm{P} \\ $$$$\left.\mathrm{1}\right).\:\:\mathrm{xy}+\mathrm{16}=\mathrm{0}\:\rightarrow\mathrm{P}\left(−\mathrm{2},\mathrm{8}\right) \\ $$$$\left.\mathrm{2}\right).\:\:\mathrm{y}^{\mathrm{2}} −\mathrm{4x}^{\mathrm{2}} =\mathrm{5}\rightarrow\mathrm{P}\left(−\mathrm{1},\mathrm{3}\right) \\ $$$$\left.\mathrm{3}\right).\:\:\mathrm{2x}^{\mathrm{3}} −\mathrm{x}^{\mathrm{2}} \mathrm{y}+\mathrm{y}^{\mathrm{3}} −\mathrm{1}=\mathrm{0}\rightarrow\mathrm{P}\left(\mathrm{2},−\mathrm{3}\right) \\ $$$$\left.\mathrm{4}\right).\:\:\mathrm{3y}^{\mathrm{4}} +\mathrm{4x}−\mathrm{x}^{\mathrm{2}} \mathrm{sin}\:\mathrm{y}−\mathrm{4}=\mathrm{0}\rightarrow\mathrm{P}\left(\mathrm{1},\mathrm{0}\right) \\ $$$$\left.\mathrm{5}\right).\:\:\mathrm{y}^{\mathrm{4}} +\mathrm{3}\:\mathrm{y}−\mathrm{4x}^{\mathrm{2}} =\mathrm{5x}+\mathrm{1}\rightarrow\mathrm{P}\left(\mathrm{1},−\mathrm{2}\right) \\ $$

Question Number 156103 Answers: 0 Comments: 0

Question Number 156102 Answers: 0 Comments: 0

Question Number 156086 Answers: 0 Comments: 4

ψ^((1)) ((1/6)) - ψ^((1)) ((5/6)) = 10ψ^((1)) ((1/3)) - ((20)/3)π^2

$$\psi^{\left(\mathrm{1}\right)} \left(\frac{\mathrm{1}}{\mathrm{6}}\right)\:-\:\psi^{\left(\mathrm{1}\right)} \left(\frac{\mathrm{5}}{\mathrm{6}}\right)\:=\:\mathrm{10}\psi^{\left(\mathrm{1}\right)} \left(\frac{\mathrm{1}}{\mathrm{3}}\right)\:-\:\frac{\mathrm{20}}{\mathrm{3}}\pi^{\mathrm{2}} \\ $$$$ \\ $$

Question Number 156085 Answers: 0 Comments: 0

Solve for real numbers: (sin2x + 4cos^2 x + 1)(cos5x - cosx)<0

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\left(\mathrm{sin2x}\:+\:\mathrm{4cos}^{\mathrm{2}} \mathrm{x}\:+\:\mathrm{1}\right)\left(\mathrm{cos5x}\:-\:\mathrm{cosx}\right)<\mathrm{0} \\ $$$$ \\ $$

Question Number 156082 Answers: 0 Comments: 0

0< α <(π/2) (( sin(α)))^(1/( 3)) + ((cos(α))^(1/3) )= (( tan(α)))^(1/3) (( tan (α ) + cot (α ))/2) =?

$$ \\ $$$$\:\:\:\:\:\mathrm{0}<\:\alpha\:<\frac{\pi}{\mathrm{2}}\:\:\: \\ $$$$\left.\:\:\sqrt[{\:\mathrm{3}}]{\:{sin}\left(\alpha\right)}\:+\:\sqrt[{\mathrm{3}}]{{cos}\left(\alpha\right.}\right)=\:\sqrt[{\mathrm{3}}]{\:{tan}\left(\alpha\right)} \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\frac{\:{tan}\:\left(\alpha\:\right)\:+\:{cot}\:\left(\alpha\:\right)}{\mathrm{2}}\:=? \\ $$

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