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Question Number 170014 Answers: 1 Comments: 0

Question Number 170003 Answers: 1 Comments: 1

prove that Σ_(n=1) ^∞ (((−1)^(n−1) )/n^2 )=(π^2 /(12))

$${prove}\:{that} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{n}^{\mathrm{2}} }=\frac{\pi^{\mathrm{2}} }{\mathrm{12}} \\ $$

Question Number 169989 Answers: 0 Comments: 0

Prove or disprove: For any extension E of a field F, F(u)=F[u] ∀ u∈E. Where F(u) is a smallest subfield of E containing F and u and F[u]={f(u)∣f(x)∈F[x]}, F[x] is a polynomial ring over F.

$$ \\ $$$$\mathrm{Prove}\:\mathrm{or}\:\mathrm{disprove}: \\ $$$$\mathrm{For}\:\mathrm{any}\:\mathrm{extension}\:{E}\:\mathrm{of}\:\mathrm{a}\:\mathrm{field}\:{F}, \\ $$$${F}\left({u}\right)={F}\left[{u}\right]\:\:\:\:\forall\:{u}\in{E}. \\ $$$$\mathrm{Where}\:{F}\left({u}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{smallest}\:\mathrm{subfield} \\ $$$$\mathrm{of}\:{E}\:\mathrm{containing}\:{F}\:\mathrm{and}\:{u}\:\mathrm{and} \\ $$$${F}\left[{u}\right]=\left\{{f}\left({u}\right)\mid{f}\left({x}\right)\in{F}\left[{x}\right]\right\},\:{F}\left[{x}\right]\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{polynomial}\:\mathrm{ring}\:\mathrm{over}\:{F}. \\ $$

Question Number 169987 Answers: 1 Comments: 0

Question Number 169986 Answers: 0 Comments: 0

(x + 2)^(2x − 3) > 1

$$\left({x}\:+\:\mathrm{2}\right)^{\mathrm{2}{x}\:−\:\mathrm{3}} \:>\:\mathrm{1} \\ $$

Question Number 169982 Answers: 0 Comments: 0

$$ \\ $$

Question Number 169977 Answers: 1 Comments: 0

Question Number 169974 Answers: 0 Comments: 1

Question Number 169973 Answers: 1 Comments: 0

Question Number 169972 Answers: 0 Comments: 0

Question Number 169969 Answers: 1 Comments: 0

Question Number 169966 Answers: 1 Comments: 0

lim_(x→0) ((sin (tan x)−tan (sin x))/(2x cos (tan x)−2x cos (sin x)+x^5 )) =?

$$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{tan}\:{x}\right)−\mathrm{tan}\:\left(\mathrm{sin}\:{x}\right)}{\mathrm{2}{x}\:\mathrm{cos}\:\left(\mathrm{tan}\:{x}\right)−\mathrm{2}{x}\:\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)+{x}^{\mathrm{5}} }\:=? \\ $$

Question Number 169949 Answers: 0 Comments: 7

Question Number 169947 Answers: 2 Comments: 1

Question Number 169944 Answers: 0 Comments: 1

Question Number 169945 Answers: 1 Comments: 5

Question Number 169942 Answers: 0 Comments: 0

Question Number 170006 Answers: 0 Comments: 0

Question Number 170005 Answers: 2 Comments: 3

Question Number 170004 Answers: 0 Comments: 0

q(x,y,z)=xy+4xz+3yz determier la reduction de gauss en carre

$${q}\left({x},{y},{z}\right)={xy}+\mathrm{4}{xz}+\mathrm{3}{yz} \\ $$$${determier}\:{la}\:{reduction}\:{de}\:{gauss}\:{en}\:{carre} \\ $$

Question Number 169932 Answers: 0 Comments: 0

if x+(1/x)=cosθ find x^n +(1/x^n ) interm of θ

$${if}\:{x}+\frac{\mathrm{1}}{{x}}={cos}\theta\:\:{find} \\ $$$${x}^{{n}} +\frac{\mathrm{1}}{{x}^{{n}} }\:{interm}\:{of}\:\theta \\ $$

Question Number 169930 Answers: 0 Comments: 0

find f(α)=∫_0 ^1 ((arctan(αx))/(1+x^2 ))dx

$${find}\:{f}\left(\alpha\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{arctan}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 169925 Answers: 0 Comments: 0

Question Number 169924 Answers: 0 Comments: 3

Question Number 169923 Answers: 0 Comments: 0

Σ_(d∣6) d=?

$$\underset{{d}\mid\mathrm{6}} {\sum}{d}=? \\ $$

Question Number 169922 Answers: 1 Comments: 0

Let f(x)=((2x−7)/(x+1)) . Compute f^(1989) (x). note f^2 (x)= f(f(x))

$$\:\:{Let}\:{f}\left({x}\right)=\frac{\mathrm{2}{x}−\mathrm{7}}{{x}+\mathrm{1}}\:.\:{Compute}\:{f}^{\mathrm{1989}} \left({x}\right). \\ $$$$\:{note}\:{f}^{\mathrm{2}} \left({x}\right)=\:{f}\left({f}\left({x}\right)\right) \\ $$

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