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Question Number 89530 Answers: 0 Comments: 2

F which is the set of funtions from R to R is a vectorial space and G(a part of F) is the set of odd functions such as G={ f ∈ F/∀ x∈ R, f(x)=−f(−x)} 1) Show that G is sub vector space of F in R.

$$\mathrm{F}\:\mathrm{which}\:\mathrm{is}\:\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{funtions}\:\mathrm{from}\:\mathbb{R}\:\mathrm{to}\:\mathbb{R}\: \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{vectorial}\:\mathrm{space}\:\mathrm{and}\:\mathrm{G}\left(\mathrm{a}\:\mathrm{part}\:\mathrm{of}\:\mathrm{F}\right)\:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{odd}\:\mathrm{functions}\:\mathrm{such}\:\mathrm{as} \\ $$$$\mathrm{G}=\left\{\:{f}\:\in\:\mathrm{F}/\forall\:\mathrm{x}\in\:\mathbb{R},\:{f}\left({x}\right)=−{f}\left(−{x}\right)\right\} \\ $$$$\left.\mathrm{1}\right)\:{S}\mathrm{how}\:\mathrm{that}\:\mathrm{G}\:\mathrm{is}\:\mathrm{sub}\:\mathrm{vector}\:\mathrm{space}\:\mathrm{of}\:\mathrm{F} \\ $$$$\mathrm{in}\:\mathbb{R}. \\ $$

Question Number 89586 Answers: 1 Comments: 0

2018^(2019) −2019^(2018 ) ≡? (mod 4)

$$ \\ $$$$\mathrm{2018}^{\mathrm{2019}} −\mathrm{2019}^{\mathrm{2018}\:} \equiv?\:\left({mod}\:\mathrm{4}\right) \\ $$

Question Number 89513 Answers: 0 Comments: 21

i open this test post to see if i can edit or delete it later.

$${i}\:{open}\:{this}\:{test}\:{post}\:{to}\:{see}\:{if}\:{i}\:{can} \\ $$$${edit}\:{or}\:{delete}\:{it}\:{later}. \\ $$

Question Number 89505 Answers: 1 Comments: 0

Question Number 89496 Answers: 2 Comments: 0

Question Number 89493 Answers: 0 Comments: 1

Question Number 89560 Answers: 0 Comments: 1

without use intergration by party ∫_0 ^(π/4) e^θ cos 2θ dθ

$${without}\:{use}\:{intergration} \\ $$$${by}\:{party} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {e}^{\theta} \mathrm{cos}\:\mathrm{2}\theta\:{d}\theta \\ $$

Question Number 89490 Answers: 0 Comments: 0

lim_(x→∞) xlnxln(((ln(x+1))/(lnx)))=?

$$\underset{{x}\rightarrow\infty} {{lim}xlnxln}\left(\frac{{ln}\left({x}+\mathrm{1}\right)}{{lnx}}\right)=? \\ $$

Question Number 89489 Answers: 0 Comments: 2

∫_(−1) ^4 x(√(×+5 ))dx

$$\int_{−\mathrm{1}} ^{\mathrm{4}} \mathrm{x}\sqrt{×+\mathrm{5}\:}\mathrm{dx} \\ $$

Question Number 89487 Answers: 0 Comments: 1

∫_(−1) ^3 (x^2 /(√(x+2))) dx

$$\int_{−\mathrm{1}} ^{\mathrm{3}} \frac{\mathrm{x}^{\mathrm{2}} }{\sqrt{\mathrm{x}+\mathrm{2}}}\:\mathrm{dx} \\ $$

Question Number 89482 Answers: 0 Comments: 7

URGENT ! to TINKUTARA developers: because i didn′t get notification, i have updated the app. but since the update, i can′t either edit my own posts or delete them. i am using a Huawei P20, Android 9.

$${URGENT}\:! \\ $$$${to}\:{TINKUTARA}\:{developers}: \\ $$$${because}\:{i}\:{didn}'{t}\:{get}\:{notification},\:{i} \\ $$$${have}\:{updated}\:{the}\:{app}.\:{but}\:{since}\:{the} \\ $$$${update},\:{i}\:{can}'{t}\:{either}\:{edit}\:{my}\:{own} \\ $$$${posts}\:{or}\:{delete}\:{them}. \\ $$$${i}\:{am}\:{using}\:{a}\:{Huawei}\:{P}\mathrm{20},\:{Android}\:\mathrm{9}. \\ $$

Question Number 89461 Answers: 2 Comments: 0

Question Number 89456 Answers: 1 Comments: 0

(log_x (6))^2 + (log_(1/6) ((1/x)))^2 + log_(1/(√x)) ((1/6)) + log_(√6) (x) + (3/4) = 0

$$\left(\mathrm{log}_{{x}} \left(\mathrm{6}\right)\right)^{\mathrm{2}} \:+\:\left(\mathrm{log}_{\frac{\mathrm{1}}{\mathrm{6}}} \left(\frac{\mathrm{1}}{{x}}\right)\right)^{\mathrm{2}} +\: \\ $$$$\mathrm{log}_{\frac{\mathrm{1}}{\sqrt{{x}}}} \left(\frac{\mathrm{1}}{\mathrm{6}}\right)\:+\:\mathrm{log}_{\sqrt{\mathrm{6}}} \:\left({x}\right)\:+\:\frac{\mathrm{3}}{\mathrm{4}}\:=\:\mathrm{0} \\ $$

Question Number 89454 Answers: 0 Comments: 1

Question Number 89451 Answers: 1 Comments: 0

log_5 ((3−x)(x^2 +2)) ≥ log_5 (x^2 −7x+12)+log_5 (5−x)

$$\mathrm{log}_{\mathrm{5}} \:\left(\left(\mathrm{3}−{x}\right)\left({x}^{\mathrm{2}} +\mathrm{2}\right)\right)\:\geqslant\:\mathrm{log}_{\mathrm{5}} \left({x}^{\mathrm{2}} −\mathrm{7}{x}+\mathrm{12}\right)+\mathrm{log}_{\mathrm{5}} \left(\mathrm{5}−{x}\right) \\ $$

Question Number 89446 Answers: 0 Comments: 1

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Question Number 89592 Answers: 1 Comments: 2

cos(x)=k {−1≤k<0}

$${cos}\left({x}\right)={k}\: \\ $$$$\left\{−\mathrm{1}\leqslant{k}<\mathrm{0}\right\} \\ $$

Question Number 89596 Answers: 0 Comments: 1

Question Number 89593 Answers: 0 Comments: 5

show that ∫_0 ^(π/2) ln(sec(x)) ln(csc(x)) dx=((π^2 ln^2 (2))/2)−(π^4 /(48))

$${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({sec}\left({x}\right)\right)\:{ln}\left({csc}\left({x}\right)\right)\:{dx}=\frac{\pi^{\mathrm{2}} \:{ln}^{\mathrm{2}} \left(\mathrm{2}\right)}{\mathrm{2}}−\frac{\pi^{\mathrm{4}} }{\mathrm{48}} \\ $$

Question Number 89425 Answers: 0 Comments: 0

∫_1 ^4 (√(1+((y^3 /2)−(1/2)y^(−1) )^2 )) dy

$$\int_{\mathrm{1}} ^{\mathrm{4}} \sqrt{\mathrm{1}+\left(\frac{{y}^{\mathrm{3}} }{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}{y}^{−\mathrm{1}} \right)^{\mathrm{2}} }\:{dy} \\ $$$$ \\ $$

Question Number 89422 Answers: 1 Comments: 1

Question Number 89415 Answers: 1 Comments: 4

Question Number 89412 Answers: 0 Comments: 8

Question Number 89399 Answers: 0 Comments: 11

Hi. A ballot box contains 3 red balls, 4 blues balls and 5 white balls. we draw successively 3 balls in ballot box by re−puting the drawn balls. 1)Calculate the number of draws containing one ball of each color.

$$\mathrm{Hi}. \\ $$$$\mathrm{A}\:\mathrm{ballot}\:\mathrm{box}\:\mathrm{contains}\:\mathrm{3}\:\mathrm{red}\:\mathrm{balls},\:\mathrm{4}\:\mathrm{blues} \\ $$$$\mathrm{balls}\:\mathrm{and}\:\mathrm{5}\:\mathrm{white}\:\mathrm{balls}. \\ $$$$\mathrm{we}\:\mathrm{draw}\:\mathrm{successively}\:\mathrm{3}\:\mathrm{balls}\:\mathrm{in}\:\mathrm{ballot}\:\mathrm{box}\: \\ $$$$\mathrm{by}\:\mathrm{re}−\mathrm{puting}\:\mathrm{the}\:\mathrm{drawn}\:\mathrm{balls}. \\ $$$$\left.\mathrm{1}\right)\mathrm{Calculate}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{draws}\: \\ $$$$\mathrm{containing}\:\mathrm{one}\:\mathrm{ball}\:\mathrm{of}\:\mathrm{each}\:\mathrm{color}. \\ $$

Question Number 89385 Answers: 1 Comments: 1

Question Number 89384 Answers: 0 Comments: 3

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