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Question Number 170014 Answers: 1 Comments: 0
Question Number 170003 Answers: 1 Comments: 1
$${prove}\:{that} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{n}^{\mathrm{2}} }=\frac{\pi^{\mathrm{2}} }{\mathrm{12}} \\ $$
Question Number 169989 Answers: 0 Comments: 0
$$ \\ $$$$\mathrm{Prove}\:\mathrm{or}\:\mathrm{disprove}: \\ $$$$\mathrm{For}\:\mathrm{any}\:\mathrm{extension}\:{E}\:\mathrm{of}\:\mathrm{a}\:\mathrm{field}\:{F}, \\ $$$${F}\left({u}\right)={F}\left[{u}\right]\:\:\:\:\forall\:{u}\in{E}. \\ $$$$\mathrm{Where}\:{F}\left({u}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{smallest}\:\mathrm{subfield} \\ $$$$\mathrm{of}\:{E}\:\mathrm{containing}\:{F}\:\mathrm{and}\:{u}\:\mathrm{and} \\ $$$${F}\left[{u}\right]=\left\{{f}\left({u}\right)\mid{f}\left({x}\right)\in{F}\left[{x}\right]\right\},\:{F}\left[{x}\right]\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{polynomial}\:\mathrm{ring}\:\mathrm{over}\:{F}. \\ $$
Question Number 169987 Answers: 1 Comments: 0
Question Number 169986 Answers: 0 Comments: 0
$$\left({x}\:+\:\mathrm{2}\right)^{\mathrm{2}{x}\:−\:\mathrm{3}} \:>\:\mathrm{1} \\ $$
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
$$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{tan}\:{x}\right)−\mathrm{tan}\:\left(\mathrm{sin}\:{x}\right)}{\mathrm{2}{x}\:\mathrm{cos}\:\left(\mathrm{tan}\:{x}\right)−\mathrm{2}{x}\:\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)+{x}^{\mathrm{5}} }\:=? \\ $$
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
$${q}\left({x},{y},{z}\right)={xy}+\mathrm{4}{xz}+\mathrm{3}{yz} \\ $$$${determier}\:{la}\:{reduction}\:{de}\:{gauss}\:{en}\:{carre} \\ $$
Question Number 169932 Answers: 0 Comments: 0
$${if}\:{x}+\frac{\mathrm{1}}{{x}}={cos}\theta\:\:{find} \\ $$$${x}^{{n}} +\frac{\mathrm{1}}{{x}^{{n}} }\:{interm}\:{of}\:\theta \\ $$
Question Number 169930 Answers: 0 Comments: 0
$${find}\:{f}\left(\alpha\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{arctan}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$
Question Number 169925 Answers: 0 Comments: 0
Question Number 169924 Answers: 0 Comments: 3
Question Number 169923 Answers: 0 Comments: 0
$$\underset{{d}\mid\mathrm{6}} {\sum}{d}=? \\ $$
Question Number 169922 Answers: 1 Comments: 0
$$\:\:{Let}\:{f}\left({x}\right)=\frac{\mathrm{2}{x}−\mathrm{7}}{{x}+\mathrm{1}}\:.\:{Compute}\:{f}^{\mathrm{1989}} \left({x}\right). \\ $$$$\:{note}\:{f}^{\mathrm{2}} \left({x}\right)=\:{f}\left({f}\left({x}\right)\right) \\ $$
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