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Question Number 36969 Answers: 1 Comments: 0
$$\left[\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{2}.\mathrm{2}^{\mathrm{3}} .\mathrm{2}^{\mathrm{5}} .....\mathrm{2}^{\mathrm{n}−\mathrm{1}} .\mathrm{3}^{\mathrm{2}} .\mathrm{3}^{\mathrm{4}} .....\mathrm{3}^{\mathrm{n}} \right)^{\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} +\mathrm{1}}} \right]^{\mathrm{4}} =? \\ $$
Question Number 36905 Answers: 0 Comments: 0
$${p}\:{is}\:{apolynom}\:{with}\:{n}\:{roots}\:{differents} \\ $$$${let}\:{Q}\:=\:{p}^{\mathrm{2}} \:+{p}^{'} \:\:\:\:{let}\:\alpha\:{the}\:{number}\:{of}\:{roots}\:{of} \\ $$$${Q}\:{prove}\:{that}\:\:\:{n}−\mathrm{1}\leqslant\alpha\leqslant{n}+\mathrm{1}\:. \\ $$
Question Number 36904 Answers: 0 Comments: 1
$$\left.\mathrm{1}\right){decompose}\:{inside}\:{C}\left[{x}\right] \\ $$$${p}\left({x}\right)={x}^{\mathrm{2}{n}} \:−\mathrm{2}\left({cos}\alpha\right){x}^{{n}} \:+\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{decopose}\:{p}\left({x}\right){inside}\:{R}\left[{x}\right] \\ $$
Question Number 36903 Answers: 0 Comments: 0
$${prove}\:{that}\:\:\mathrm{2}^{{n}+\mathrm{1}} \:{divide}\:\left[\left(\mathrm{1}+\sqrt{\mathrm{3}}\right)^{\mathrm{2}{n}+\mathrm{1}} \right]\: \\ $$$$\left[{x}\right]\:{mean}\:{integr}\:{part}\:{of}\:{x} \\ $$
Question Number 36892 Answers: 1 Comments: 1
$$\mathrm{2}.\:\int\left[\sqrt{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)/\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}\right]{dx}=? \\ $$
Question Number 36886 Answers: 0 Comments: 1
Question Number 36884 Answers: 0 Comments: 0
$$\mathrm{1}.\:\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{cueved}\:\mathrm{line}\:\mathrm{which}\:\mathrm{is}\:\mathrm{made}\:\mathrm{by}\:\mathrm{a} \\ $$$$\mathrm{fixed}\:\mathrm{point}\:\mathrm{in}\:\mathrm{the}\:\mathrm{boundary}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{moving}\:\mathrm{circular}\:\mathrm{object}\:\mathrm{in}\:\mathrm{respect}\:\mathrm{to} \\ $$$$\mathrm{an}\:\mathrm{another}\:\mathrm{fiexd}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the}\:\mathrm{way}\:\mathrm{of} \\ $$$$\mathrm{moving}? \\ $$
Question Number 36880 Answers: 1 Comments: 3
Question Number 36877 Answers: 0 Comments: 0
Question Number 36876 Answers: 0 Comments: 0
Question Number 36874 Answers: 0 Comments: 0
Question Number 36873 Answers: 0 Comments: 0
Question Number 36872 Answers: 0 Comments: 0
Question Number 36871 Answers: 0 Comments: 0
Question Number 36867 Answers: 0 Comments: 0
Question Number 36865 Answers: 0 Comments: 0
Question Number 36862 Answers: 0 Comments: 1
Question Number 36861 Answers: 0 Comments: 0
Question Number 36853 Answers: 0 Comments: 2
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{laplace}\:\mathrm{of}\:\:\:\:\:\mathrm{L}\left\{\frac{\mathrm{e}^{−\mathrm{at}} \:−\:\mathrm{e}^{−\mathrm{bt}} }{\mathrm{t}}\right\} \\ $$
Question Number 36852 Answers: 0 Comments: 0
Question Number 36851 Answers: 1 Comments: 0
Question Number 36855 Answers: 1 Comments: 1
Question Number 36846 Answers: 1 Comments: 6
Question Number 36845 Answers: 0 Comments: 0
Question Number 36844 Answers: 1 Comments: 0
$$\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{4}\:\mathrm{digit}\:\mathrm{even}\:\mathrm{numbers}\:\mathrm{formed}\:\mathrm{from}\:\mathrm{the}\:\mathrm{digit}\:\:\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4} \\ $$
Question Number 36843 Answers: 1 Comments: 1
$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left({x}^{{x}^{{x}^{.....} } } \right) \\ $$
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