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Question Number 213216    Answers: 1   Comments: 0

Question Number 213215    Answers: 0   Comments: 0

Question Number 213208    Answers: 1   Comments: 0

Let f(x)∈Q[x] irreducible of degree n and K it′s Splitting Field over Q Prove that if Gal(K\Q) is Abeilan then ∣Gal(K\Q)∣=n How can i prove this???

$$\mathrm{Let}\:{f}\left({x}\right)\in\mathbb{Q}\left[{x}\right]\:\mathrm{irreducible}\:\mathrm{of}\:\mathrm{degree}\:{n} \\ $$$$\mathrm{and}\:{K}\:\mathrm{it}'\mathrm{s}\:\mathrm{Splitting}\:\mathrm{Field}\:\mathrm{over}\:\mathbb{Q} \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{if}\:\mathrm{Gal}\left({K}\backslash\mathbb{Q}\right)\:\mathrm{is}\:\mathrm{Abeilan} \\ $$$$\mathrm{then}\:\mid\mathrm{Gal}\left({K}\backslash\mathbb{Q}\right)\mid={n} \\ $$$$\mathrm{How}\:\mathrm{can}\:\mathrm{i}\:\mathrm{prove}\:\mathrm{this}??? \\ $$

Question Number 213201    Answers: 2   Comments: 1

Question Number 213198    Answers: 1   Comments: 0

Question Number 213203    Answers: 4   Comments: 0

G

$$\:\:\:\:\:\:\cancel{\underline{\underbrace{\mathscr{G}}}} \\ $$

Question Number 213175    Answers: 4   Comments: 0

we can find tan120 by tan(180−60) but can not find by tan(90+30) why?

$${we}\:{can}\:{find}\:{tan}\mathrm{120}\:{by}\:{tan}\left(\mathrm{180}−\mathrm{60}\right) \\ $$$${but}\:{can}\:{not}\:{find}\:{by}\:{tan}\left(\mathrm{90}+\mathrm{30}\right)\:{why}? \\ $$

Question Number 213173    Answers: 3   Comments: 1

Question Number 213169    Answers: 1   Comments: 0

prove lim_(n→∞) ∫_0 ^1 (n/(1+n^2 x^2 ))e^x^2 dx=(π/2).

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{prove} \\ $$$$\:\:\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{n}}{\mathrm{1}+{n}^{\mathrm{2}} {x}^{\mathrm{2}} }{e}^{{x}^{\mathrm{2}} } {dx}=\frac{\pi}{\mathrm{2}}. \\ $$

Question Number 213139    Answers: 3   Comments: 0

Question Number 213138    Answers: 2   Comments: 1

Question Number 213128    Answers: 3   Comments: 0

lim_(x→0^(+ ) ) (2/(1+e^(−(1/x)) ))

$$\boldsymbol{\mathrm{lim}}_{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}^{+\:} } \frac{\mathrm{2}}{\mathrm{1}+\boldsymbol{\mathrm{e}}^{−\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}} } \\ $$

Question Number 213123    Answers: 1   Comments: 0

factoriser x^5 +x^3 +x^2 −2x−1

$$\mathrm{factoriser} \\ $$$$\boldsymbol{\mathrm{x}}^{\mathrm{5}} +\boldsymbol{\mathrm{x}}^{\mathrm{3}} +\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{\mathrm{x}}−\mathrm{1} \\ $$

Question Number 213119    Answers: 2   Comments: 1

determiner a et b par ; AB ⊥BC { ((AM =5)),((AC =16)) :}

$$\mathrm{determiner}\:\boldsymbol{\mathrm{a}}\:\mathrm{et}\:\boldsymbol{\mathrm{b}}\:\mathrm{par}\:\:\:;\:\:\mathrm{AB}\:\bot\mathrm{BC} \\ $$$$\begin{cases}{\mathrm{AM}\:=\mathrm{5}}\\{\mathrm{AC}\:\:=\mathrm{16}}\end{cases} \\ $$

Question Number 213114    Answers: 2   Comments: 0

÷

$$\:\:\:\:\:\:\:\:\underline{\boldsymbol{\div}} \\ $$

Question Number 213109    Answers: 3   Comments: 0

lim_(x→∞) ((√(x+(√(x+(√x)))))/( (√(x+1))))=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\sqrt{{x}+\sqrt{{x}+\sqrt{{x}}}}}{\:\sqrt{{x}+\mathrm{1}}}=? \\ $$

Question Number 213103    Answers: 0   Comments: 1

Hey tinku tara, I couldn′t graph the equation.

$$\mathrm{Hey}\:\mathrm{tinku}\:\mathrm{tara}, \\ $$$$\mathrm{I}\:\mathrm{couldn}'\mathrm{t}\:\mathrm{graph}\:\mathrm{the}\:\mathrm{equation}. \\ $$

Question Number 213100    Answers: 1   Comments: 1

Find this numeric expression using: The arithmetic division rule a÷b(c)=a÷b×c, The solvable incorrect syntax rule (a)b=a×b, where b is a number: 12÷4(10−8+1)2÷6×2=?

$$\mathrm{Find}\:\mathrm{this}\:\mathrm{numeric}\:\mathrm{expression}\:\mathrm{using}: \\ $$$$\mathrm{The}\:\mathrm{arithmetic}\:\mathrm{division}\:\mathrm{rule}\:{a}\boldsymbol{\div}{b}\left({c}\right)={a}\boldsymbol{\div}{b}×{c}, \\ $$$$\mathrm{The}\:\mathrm{solvable}\:\mathrm{incorrect}\:\mathrm{syntax}\:\mathrm{rule}\:\left({a}\right){b}={a}×{b},\:\mathrm{where}\:{b}\:\mathrm{is}\:\mathrm{a}\:\mathrm{number}: \\ $$$$\mathrm{12}\boldsymbol{\div}\mathrm{4}\left(\mathrm{10}−\mathrm{8}+\mathrm{1}\right)\mathrm{2}\boldsymbol{\div}\mathrm{6}×\mathrm{2}=? \\ $$

Question Number 213099    Answers: 1   Comments: 0

(1/2)(x−1)−(x−3)=(1/3)(x+3)+(1/6) x=...

$$\frac{\mathrm{1}}{\mathrm{2}}\left({x}−\mathrm{1}\right)−\left({x}−\mathrm{3}\right)=\frac{\mathrm{1}}{\mathrm{3}}\left({x}+\mathrm{3}\right)+\frac{\mathrm{1}}{\mathrm{6}} \\ $$$${x}=... \\ $$

Question Number 213098    Answers: 3   Comments: 0

∫((3x+2)/(5x^2 +2x+3))dx=?

$$\int\frac{\mathrm{3}{x}+\mathrm{2}}{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{3}}\mathrm{d}{x}=? \\ $$

Question Number 213097    Answers: 1   Comments: 0

Uhhhh. can you guys solve Partial differantial equation ▽^2 𝛗=0 Cylinderical Laplacian case ▽^2 =(1/ρ)∙((∂ )/∂ρ)(ρ((∂ )/∂ρ))+((1/ρ))^2 (∂^2 /∂φ^2 )+((∂^2 )/∂z^2 ) Spherical Laplacian case ▽^2 =((1/r))^2 ((∂ )/∂r)(r^2 ((∂ )/∂r))+(1/(r^2 sin(θ)))∙((∂ )/∂θ)(sin(θ)((∂ )/∂θ))+(1/(r^2 sin^2 (θ)))∙(∂^2 /∂ϕ^2 )

$$\mathrm{Uhhhh}. \\ $$$$\mathrm{can}\:\mathrm{you}\:\mathrm{guys}\:\mathrm{solve}\:\mathrm{Partial}\:\mathrm{differantial}\:\mathrm{equation} \\ $$$$\bigtriangledown^{\mathrm{2}} \boldsymbol{\phi}=\mathrm{0} \\ $$$$\mathrm{Cylinderical}\:\mathrm{Laplacian}\:\mathrm{case} \\ $$$$\bigtriangledown^{\mathrm{2}} =\frac{\mathrm{1}}{\rho}\centerdot\frac{\partial\:\:}{\partial\rho}\left(\rho\frac{\partial\:\:}{\partial\rho}\right)+\left(\frac{\mathrm{1}}{\rho}\right)^{\mathrm{2}} \frac{\partial^{\mathrm{2}} \:}{\partial\phi^{\mathrm{2}} }+\frac{\partial^{\mathrm{2}} \:\:}{\partial{z}^{\mathrm{2}} } \\ $$$$\mathrm{Spherical}\:\mathrm{Laplacian}\:\mathrm{case} \\ $$$$\bigtriangledown^{\mathrm{2}} =\left(\frac{\mathrm{1}}{{r}}\right)^{\mathrm{2}} \frac{\partial\:\:}{\partial{r}}\left({r}^{\mathrm{2}} \frac{\partial\:\:}{\partial{r}}\right)+\frac{\mathrm{1}}{{r}^{\mathrm{2}} \mathrm{sin}\left(\theta\right)}\centerdot\frac{\partial\:\:}{\partial\theta}\left(\mathrm{sin}\left(\theta\right)\frac{\partial\:\:}{\partial\theta}\right)+\frac{\mathrm{1}}{{r}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \left(\theta\right)}\centerdot\frac{\partial^{\mathrm{2}} \:}{\partial\varphi^{\mathrm{2}} } \\ $$

Question Number 213096    Answers: 1   Comments: 0

Hi nikif90 can you please look at q212921 and provide details on the problem that are facimg

$$\mathrm{Hi}\:\mathrm{nikif90} \\ $$$$\mathrm{can}\:\mathrm{you}\:\mathrm{please}\:\mathrm{look}\:\mathrm{at}\:\mathrm{q212921}\:\mathrm{and} \\ $$$$\mathrm{provide}\:\mathrm{details}\:\mathrm{on}\:\mathrm{the}\:\mathrm{problem}\:\mathrm{that} \\ $$$$\mathrm{are}\:\mathrm{facimg} \\ $$

Question Number 213084    Answers: 4   Comments: 0

If 0 < x < (π/2) then prove sin(cosx) < cosx < cos(sinx). not using graph.

$$\mathrm{If}\:\mathrm{0}\:<\:{x}\:<\:\frac{\pi}{\mathrm{2}}\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{sin}\left(\mathrm{cos}{x}\right)\:<\:\mathrm{cos}{x}\:<\:\mathrm{cos}\left(\mathrm{sin}{x}\right). \\ $$$$\mathrm{not}\:\mathrm{using}\:\mathrm{graph}. \\ $$

Question Number 213082    Answers: 1   Comments: 0

Question Number 213081    Answers: 1   Comments: 0

evaluate ∫_0 ^( ∞) ((tanh((1/2)z)csch(z))/z)dz 1) Complex integral 2) Feynman trick

$$\mathrm{evaluate} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:\:\:\:\frac{\mathrm{tanh}\left(\frac{\mathrm{1}}{\mathrm{2}}{z}\right)\mathrm{csch}\left({z}\right)}{{z}}\mathrm{d}{z} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Complex}\:\mathrm{integral} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{Feynman}\:\mathrm{trick} \\ $$

Question Number 213073    Answers: 1   Comments: 0

L=lim_(x→0) {(1/x^2 )tan^(−1) ((√(1+(x^2 /a^2 )))−1)}

$${L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\mathrm{tan}^{−\mathrm{1}} \left(\sqrt{\mathrm{1}+\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }}−\mathrm{1}\right)\right\} \\ $$

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