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Question Number 145979 Answers: 1 Comments: 0

sin^2 x−4cos^3 x−1=2cos^2 x+2cos x−2cos xsin^2 x x=?

$$\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}−\mathrm{4cos}\:^{\mathrm{3}} \mathrm{x}−\mathrm{1}=\mathrm{2cos}\:^{\mathrm{2}} \mathrm{x}+\mathrm{2cos}\:\mathrm{x}−\mathrm{2cos}\:\mathrm{xsin}\:^{\mathrm{2}} \mathrm{x} \\ $$$$\mathrm{x}=? \\ $$

Question Number 145975 Answers: 1 Comments: 0

∫_( 0) ^( 6) [ (√(36−x^2 ))−(6−x)]dx=?

$$\underset{\:\mathrm{0}} {\overset{\:\mathrm{6}} {\int}}\:\left[\:\sqrt{\mathrm{36}−{x}^{\mathrm{2}} }−\left(\mathrm{6}−{x}\right)\right]{dx}=? \\ $$

Question Number 146001 Answers: 1 Comments: 0

Soit p∈End(E). on pose q=id_E −p a) montrer que p est un projecteur si et seulement si q est un projecteur.. b) on suppose que p est un projecteur et on considere L={f∈End(E)/∃u∈End(E),f=u○p} et M={g∈End(E)/∃v∈End(E), g=v○q}. montrer que L et M sont des sous espaces vectoriels supplementaires de End(E)..

$$\mathrm{Soit}\:\mathrm{p}\in\mathrm{End}\left(\mathrm{E}\right).\:\mathrm{on}\:\mathrm{pose}\:\mathrm{q}=\mathrm{id}_{\mathrm{E}} −\mathrm{p} \\ $$$$\left.\mathrm{a}\right)\:\mathrm{montrer}\:\mathrm{que}\:\mathrm{p}\:\mathrm{est}\:\mathrm{un}\:\mathrm{projecteur}\:\mathrm{si}\:\mathrm{et}\: \\ $$$$\mathrm{seulement}\:\mathrm{si}\:\mathrm{q}\:\mathrm{est}\:\mathrm{un}\:\mathrm{projecteur}.. \\ $$$$\left.\mathrm{b}\right)\:\mathrm{on}\:\mathrm{suppose}\:\mathrm{que}\:\mathrm{p}\:\mathrm{est}\:\mathrm{un}\:\mathrm{projecteur}\:\mathrm{et}\:\mathrm{on} \\ $$$$\mathrm{considere}\:\mathrm{L}=\left\{\mathrm{f}\in\mathrm{End}\left(\mathrm{E}\right)/\exists\mathrm{u}\in\mathrm{End}\left(\mathrm{E}\right),\mathrm{f}=\mathrm{u}\circ\mathrm{p}\right\} \\ $$$$\mathrm{et}\:\mathrm{M}=\left\{\mathrm{g}\in\mathrm{End}\left(\mathrm{E}\right)/\exists\mathrm{v}\in\mathrm{End}\left(\mathrm{E}\right),\:\mathrm{g}=\mathrm{v}\circ\mathrm{q}\right\}. \\ $$$$\mathrm{montrer}\:\mathrm{que}\:\mathrm{L}\:\mathrm{et}\:\mathrm{M}\:\mathrm{sont}\:\mathrm{des}\:\mathrm{sous}\:\mathrm{espaces}\: \\ $$$$\mathrm{vectoriels}\:\mathrm{supplementaires}\:\mathrm{de}\:\mathrm{End}\left(\mathrm{E}\right).. \\ $$

Question Number 146000 Answers: 0 Comments: 3

Question Number 145960 Answers: 2 Comments: 0

Question Number 145954 Answers: 1 Comments: 0

1+i+i^2 +i^3 +...+i^(99) =?

$$\mathrm{1}+{i}+{i}^{\mathrm{2}} +{i}^{\mathrm{3}} +...+{i}^{\mathrm{99}} =? \\ $$

Question Number 145953 Answers: 1 Comments: 4

Question Number 145951 Answers: 1 Comments: 0

Σ_(n≥1) (((−1)^n )/n)=??

$$\underset{{n}\geqslant\mathrm{1}} {\sum}\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}}=?? \\ $$

Question Number 145947 Answers: 1 Comments: 1

Question Number 145946 Answers: 1 Comments: 0

the type of singular point of f(z)=((cos(πz))/((1−z^3 ))) is ?

$${the}\:{type}\:{of}\:{singular}\:{point}\:{of}\:{f}\left({z}\right)=\frac{{cos}\left(\pi{z}\right)}{\left(\mathrm{1}−{z}^{\mathrm{3}} \right)}\:{is}\:? \\ $$$$ \\ $$$$ \\ $$

Question Number 145944 Answers: 1 Comments: 1

Question Number 145942 Answers: 1 Comments: 0

Question Number 145941 Answers: 1 Comments: 0

find ∫_0 ^∞ e^(−3x) log(1+x^3 )dx

$${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\mathrm{3}{x}} {log}\left(\mathrm{1}+{x}^{\mathrm{3}} \right){dx} \\ $$

Question Number 145940 Answers: 0 Comments: 0

find ∫_0 ^1 e^(−x) log(1−x^4 )dx

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−{x}} {log}\left(\mathrm{1}−{x}^{\mathrm{4}} \right){dx} \\ $$

Question Number 145939 Answers: 0 Comments: 0

Ψ(x)=ch(sinx) developp Ψ at fourier serie

$$\Psi\left({x}\right)={ch}\left({sinx}\right) \\ $$$${developp}\:\Psi\:{at}\:{fourier}\:{serie} \\ $$

Question Number 145938 Answers: 1 Comments: 0

g(x)=cos(arctanx) if g(x)=Σ a_n x^n determine the sequence a_n

$${g}\left({x}\right)={cos}\left({arctanx}\right) \\ $$$${if}\:{g}\left({x}\right)=\Sigma\:{a}_{{n}} {x}^{{n}} \:{determine}\:{the} \\ $$$${sequence}\:{a}_{{n}} \\ $$

Question Number 145936 Answers: 0 Comments: 0

g(x)=arctan(cosx) developp f at fourier serie

$${g}\left({x}\right)={arctan}\left({cosx}\right) \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$

Question Number 145934 Answers: 0 Comments: 0

Question Number 145918 Answers: 1 Comments: 0

Question Number 145911 Answers: 4 Comments: 1

Question Number 145889 Answers: 0 Comments: 2

Question Number 145888 Answers: 1 Comments: 0

Question Number 145886 Answers: 0 Comments: 0

((x(√((129934)/(14348057))))/π^2 ) = e^π then ((√(x−96))/4) =?

$$\frac{\mathrm{x}\sqrt{\frac{\mathrm{129934}}{\mathrm{14348057}}}}{\pi^{\mathrm{2}} }\:=\:\mathrm{e}^{\pi} \:\mathrm{then}\: \\ $$$$\:\frac{\sqrt{\mathrm{x}−\mathrm{96}}}{\mathrm{4}}\:=?\: \\ $$

Question Number 145884 Answers: 0 Comments: 0

Question Number 146041 Answers: 3 Comments: 0

z′ = 2iz + (3−3i) geometrical representation is?

$${z}'\:=\:\mathrm{2}{iz}\:+\:\left(\mathrm{3}−\mathrm{3}{i}\right) \\ $$$${geometrical}\:{representation}\:{is}? \\ $$

Question Number 145879 Answers: 1 Comments: 0

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