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Question Number 211575 Answers: 2 Comments: 0

Question Number 211570 Answers: 0 Comments: 2

{x_n }>0 lim_(x→0) x_n ^(1/n) =a prove when a<1 lim_(x→0) x_n =0 when a>1 lim_(x→0) x_n =∞ and when a=1 what happen about x_n

$$\left\{{x}_{{n}} \right\}>\mathrm{0} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{x}_{{n}} ^{\frac{\mathrm{1}}{{n}}} ={a} \\ $$$${prove}\:{when}\:{a}<\mathrm{1}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{x}_{{n}} =\mathrm{0} \\ $$$${when}\:{a}>\mathrm{1}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{x}_{{n}} =\infty \\ $$$${and}\:{when}\:{a}=\mathrm{1}\:{what}\:{happen}\:{about}\:{x}_{{n}} \\ $$

Question Number 211567 Answers: 0 Comments: 2

if lim_(x→0) f(x)=lim_(x→0) g(x)=0 when do not use f(x) to replace g(x)

$${if}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{f}\left({x}\right)=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{g}\left({x}\right)=\mathrm{0} \\ $$$${when}\:{do}\:{not}\:{use}\:{f}\left({x}\right)\:{to}\:\:{replace}\:{g}\left({x}\right)\:\:\: \\ $$

Question Number 211566 Answers: 0 Comments: 0

certificate: Σ_(n=−∞) ^(+∞) (1/(n^4 +a^4 ))=(𝛑/( (√2)a^3 )) ((sinh((√2)a𝛑)+sin((√2)a𝛑))/( (√2)a^3 cosh((√2)a𝛑)−cos((√2)a𝛑)))

$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{certificate}: \\ $$$$\:\:\:\:\:\:\:\:\underset{\boldsymbol{{n}}=−\infty} {\overset{+\infty} {\sum}}\frac{\mathrm{1}}{\boldsymbol{{n}}^{\mathrm{4}} +\boldsymbol{{a}}^{\mathrm{4}} }=\frac{\boldsymbol{\pi}}{\:\sqrt{\mathrm{2}}\boldsymbol{{a}}^{\mathrm{3}} }\:\frac{\boldsymbol{\mathrm{si}{n}\mathrm{h}}\left(\sqrt{\mathrm{2}}\boldsymbol{{a}\pi}\right)+\boldsymbol{\mathrm{sin}}\left(\sqrt{\mathrm{2}}\boldsymbol{{a}\pi}\right)}{\:\sqrt{\mathrm{2}}\boldsymbol{{a}}^{\mathrm{3}} \boldsymbol{\mathrm{cos}{h}}\left(\sqrt{\mathrm{2}}\boldsymbol{{a}\pi}\right)−\boldsymbol{\mathrm{cos}}\left(\sqrt{\mathrm{2}}\boldsymbol{{a}\pi}\right)} \\ $$$$ \\ $$

Question Number 211564 Answers: 0 Comments: 1

certificate:Σ_(x=1) ^(90) ((sin(x^2 ))/(sin(x)))=45

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{certificate}:\underset{\boldsymbol{{x}}=\mathrm{1}} {\overset{\mathrm{90}} {\sum}}\frac{\boldsymbol{\mathrm{sin}}\left(\boldsymbol{{x}}^{\mathrm{2}} \right)}{\boldsymbol{\mathrm{sin}}\left(\boldsymbol{{x}}\right)}=\mathrm{45} \\ $$$$ \\ $$$$ \\ $$

Question Number 211563 Answers: 1 Comments: 0

1.x^3 −3x−2=0 2.e^x +x^2 −4=0

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}.\boldsymbol{{x}}^{\mathrm{3}} −\mathrm{3}\boldsymbol{{x}}−\mathrm{2}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}.\boldsymbol{{e}}^{\boldsymbol{{x}}} +\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{4}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 211574 Answers: 1 Comments: 0

{ ((x^2 +y^2 =25)),((x+2y−3=0)) :}

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\begin{cases}{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\mathrm{25}}\\{\boldsymbol{{x}}+\mathrm{2}\boldsymbol{\mathrm{y}}−\mathrm{3}=\mathrm{0}}\end{cases} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$ \\ $$

Question Number 211562 Answers: 2 Comments: 0

{ ((x^2 +y^2 =1)),((x^3 −y=0)) :}

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\begin{cases}{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\mathrm{1}}\\{\boldsymbol{{x}}^{\mathrm{3}} −\boldsymbol{\mathrm{y}}=\mathrm{0}}\end{cases} \\ $$

Question Number 211560 Answers: 0 Comments: 0

certificate: I=∫_0 ^(𝛑/2) (√(√(x^2 +ln^2 cos(x)−lncos(x)dx)))=(𝛑/2)(√(2ln2))

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{certificate}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{I}}=\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \sqrt{\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{ln}}^{\mathrm{2}} \boldsymbol{\mathrm{cos}}\left(\boldsymbol{{x}}\right)−\boldsymbol{\mathrm{lncos}}\left(\boldsymbol{{x}}\right)\boldsymbol{{dx}}}}=\frac{\boldsymbol{\pi}}{\mathrm{2}}\sqrt{\mathrm{2}\boldsymbol{\mathrm{ln}}\mathrm{2}} \\ $$$$ \\ $$

Question Number 211548 Answers: 2 Comments: 0

{ ((2x^2 +3y^2 −6xy=12)),((x^2 −y^2 =4)) :}

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\begin{cases}{\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{3}\boldsymbol{\mathrm{y}}^{\mathrm{2}} −\mathrm{6}\boldsymbol{{x}\mathrm{y}}=\mathrm{12}}\\{\boldsymbol{{x}}^{\mathrm{2}} −\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\mathrm{4}}\end{cases} \\ $$$$ \\ $$

Question Number 211546 Answers: 2 Comments: 0

∫(dx/( (√(x^2 −4x+13))))=?

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{\boldsymbol{{dx}}}{\:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{{x}}+\mathrm{13}}}=? \\ $$

Question Number 211537 Answers: 3 Comments: 0

Question Number 211535 Answers: 1 Comments: 0

Question Number 211558 Answers: 1 Comments: 0

−−−−−−−−−−−− 𝛀= Σ_(n=0) ^∞ ((1/(3n+2)) −(1/(3n+1)) )= a𝛑 ⇒ a^2 = ? −−−−−−−−−−−−

$$ \\ $$$$ \\ $$$$\:\:\:\:\:−−−−−−−−−−−− \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\Omega}=\:\underset{\boldsymbol{{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\left(\frac{\mathrm{1}}{\mathrm{3}\boldsymbol{{n}}+\mathrm{2}}\:−\frac{\mathrm{1}}{\mathrm{3}\boldsymbol{{n}}+\mathrm{1}}\:\right)=\:\boldsymbol{{a}\pi} \\ $$$$\:\:\:\:\:\:\:\Rightarrow\:\:\boldsymbol{{a}}^{\mathrm{2}} =\:? \\ $$$$\:\:\:\:\:\:\:−−−−−−−−−−−− \\ $$

Question Number 211531 Answers: 1 Comments: 0

∫_0 ^∞ (x^2 /(sinh(x)^2 ))dx.

$$\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{{x}}^{\mathrm{2}} }{\boldsymbol{\mathrm{sinh}}\left(\boldsymbol{{x}}\right)^{\mathrm{2}} }\boldsymbol{{dx}}. \\ $$

Question Number 211529 Answers: 1 Comments: 0

known:x+y=3,ask: min((√(x^2 +1))+(√(y2−4)))=?

$$\mathrm{known}:\boldsymbol{{x}}+\boldsymbol{\mathrm{y}}=\mathrm{3},\mathrm{ask}: \\ $$$$\boldsymbol{\mathrm{min}}\left(\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{1}}+\sqrt{\boldsymbol{\mathrm{y}}\mathrm{2}−\mathrm{4}}\right)=? \\ $$

Question Number 211528 Answers: 0 Comments: 2

I = ∫_0 ^( 1) (( tanh^(−1) (x^2 ))/x^( 2) ) dx= ?

$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{tanh}^{−\mathrm{1}} \:\left({x}^{\mathrm{2}} \:\right)}{{x}^{\:\mathrm{2}} }\:{dx}=\:?\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 211524 Answers: 1 Comments: 0

Solve for x: x^x = 4x

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}:\:\:\:\mathrm{x}^{\mathrm{x}} \:\:=\:\:\mathrm{4x} \\ $$

Question Number 211520 Answers: 2 Comments: 1

determiner les valeurs de pet q sachant que −2 et 3 sont les −2 et 3 sont les racines de l equation: 2pqz^2 −5z−4(p+q)=0

$$\mathrm{determiner}\:\mathrm{les}\:\mathrm{valeurs}\:\:\mathrm{de}\:\boldsymbol{\mathrm{p}}\mathrm{et}\:\boldsymbol{\mathrm{q}}\:\mathrm{sachant}\:\mathrm{que}\:−\mathrm{2}\:\mathrm{et}\:\mathrm{3}\:\mathrm{sont}\:\mathrm{les}\: \\ $$$$−\mathrm{2}\:\mathrm{et}\:\mathrm{3}\:\:\mathrm{sont}\:\mathrm{les}\:\mathrm{racines}\:\mathrm{de}\:\mathrm{l}\:\mathrm{equation}: \\ $$$$\mathrm{2}\boldsymbol{\mathrm{pqz}}^{\mathrm{2}} −\mathrm{5}\boldsymbol{\mathrm{z}}−\mathrm{4}\left(\boldsymbol{\mathrm{p}}+\boldsymbol{\mathrm{q}}\right)=\mathrm{0} \\ $$$$ \\ $$

Question Number 211515 Answers: 0 Comments: 2

for example I say Bob is born in 1900s, there the symbol of (s) means century. what kind of word it taken from?

$${for}\:{example}\:{I}\:{say}\:{Bob}\:{is}\:{born}\:{in} \\ $$$$\mathrm{1900}{s},\:{there}\:{the}\:{symbol}\:{of}\:\left({s}\right)\:{means} \\ $$$${century}.\:{what}\:{kind}\:{of}\:{word}\:{it}\:{taken} \\ $$$${from}? \\ $$

Question Number 211513 Answers: 0 Comments: 1

why we use Ampier meter sequence with resistance in circuit?

$${why}\:{we}\:{use}\:{Ampier}\:{meter}\:{sequence} \\ $$$${with}\:{resistance}\:{in}\:{circuit}? \\ $$

Question Number 211509 Answers: 2 Comments: 0

Question Number 211508 Answers: 1 Comments: 3

If (√(1 − x^2 )) + (√(1 − y^2 )) = a(x − y) then prove that (dy/dx) = (√(((1 − y^2 )/(1 − x^2 )) )) .

$$\mathrm{If}\:\sqrt{\mathrm{1}\:−\:{x}^{\mathrm{2}} }\:+\:\sqrt{\mathrm{1}\:−\:{y}^{\mathrm{2}} }\:=\:{a}\left({x}\:−\:{y}\right)\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\frac{{dy}}{{dx}}\:=\:\sqrt{\frac{\mathrm{1}\:−\:{y}^{\mathrm{2}} }{\mathrm{1}\:−\:{x}^{\mathrm{2}} }\:}\:. \\ $$

Question Number 211502 Answers: 2 Comments: 0

If { ((f(x)=x^2 )),((g(x)=sin x)) :}, Then find (df/dg).

$$\mathrm{If}\:\begin{cases}{{f}\left({x}\right)={x}^{\mathrm{2}} }\\{{g}\left({x}\right)=\mathrm{sin}\:{x}}\end{cases}, \\ $$$$\mathrm{Then}\:\mathrm{find}\:\frac{{df}}{{dg}}. \\ $$

Question Number 211496 Answers: 1 Comments: 0

Question Number 211495 Answers: 2 Comments: 0

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