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Question Number 151747 Answers: 1 Comments: 0

let f(x)=((λ-x)/(1+x^2 )) and λ≥((-3)/4) solve in R f(f(f(x))) ≤ 0

$$\mathrm{let}\:\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\lambda-\mathrm{x}}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\:\mathrm{and}\:\:\lambda\geqslant\frac{-\mathrm{3}}{\mathrm{4}} \\ $$$$\mathrm{solve}\:\mathrm{in}\:\mathbb{R}\:\:\mathrm{f}\left(\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\right)\:\leqslant\:\mathrm{0} \\ $$

Question Number 151744 Answers: 1 Comments: 0

show that.... F := ∫_0 ^( ∞) (( sin^( 4) (x^( 2) ) )/x^( 2) ) dx = (1/8) ( 4 − (√2) )(√π) .....■ ...m.n...

$$ \\ $$$$\:\:\:\:\:\:\:\:{show}\:\:{that}.... \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathscr{F}\::=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{sin}^{\:\mathrm{4}} \:\left({x}^{\:\mathrm{2}} \:\right)\:}{{x}^{\:\mathrm{2}} }\:{dx}\:=\:\frac{\mathrm{1}}{\mathrm{8}}\:\left(\:\mathrm{4}\:−\:\sqrt{\mathrm{2}}\:\right)\sqrt{\pi}\:.....\blacksquare\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:...{m}.{n}... \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 151742 Answers: 1 Comments: 0

F (x ):= ((log (sin(x) +cos (x)))/(log (sin(2x)))) find the Domain of F ... D_( F) =?

$$\:\: \\ $$$$\:\:\:\mathrm{F}\:\left({x}\:\right):=\:\frac{{log}\:\left({sin}\left({x}\right)\:+{cos}\:\left({x}\right)\right)}{{log}\:\left({sin}\left(\mathrm{2}{x}\right)\right)} \\ $$$$\:\:{find}\:\:\:{the}\:{Domain}\:{of}\:\:\:\:\mathrm{F}\:... \\ $$$$\:\:\:\mathrm{D}_{\:\mathrm{F}} \:=? \\ $$

Question Number 151739 Answers: 0 Comments: 0

∫_0 ^( ∞) ((ln(x))/( (√(x^x +1)))) dx

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{ln}\left({x}\right)}{\:\sqrt{{x}^{{x}} +\mathrm{1}}}\:{dx} \\ $$$$\: \\ $$

Question Number 151738 Answers: 1 Comments: 0

∫_0 ^( 1) x d(e^x^2 ) how it solve

$$\int_{\mathrm{0}} ^{\:\mathrm{1}} \:{x}\:{d}\left({e}^{{x}^{\mathrm{2}} } \right) \\ $$$$ \\ $$$${how}\:{it}\:{solve}\: \\ $$

Question Number 151791 Answers: 1 Comments: 0

Question Number 151790 Answers: 1 Comments: 0

Question Number 151724 Answers: 0 Comments: 10

Question Number 151699 Answers: 2 Comments: 0

Σ_(x^3 +2022x−2021=0) (((1+x)/(1−x))) =?

$$\:\:\:\:\underset{{x}^{\mathrm{3}} +\mathrm{2022}{x}−\mathrm{2021}=\mathrm{0}} {\sum}\left(\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\right)\:=? \\ $$

Question Number 151761 Answers: 1 Comments: 0

∫_0 ^( ∞) (1/( (√(e^x +1)))) dx

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{1}}{\:\sqrt{{e}^{{x}} +\mathrm{1}}}\:{dx}\: \\ $$$$\: \\ $$

Question Number 151685 Answers: 1 Comments: 0

Find maximum value of function α(x)= (√(2x)) +(√(16−x)) +(√(35+x)) .

$$\:\:{Find}\:{maximum}\:{value}\:{of}\:{function} \\ $$$$\:\:\alpha\left({x}\right)=\:\sqrt{\mathrm{2}{x}}\:+\sqrt{\mathrm{16}−{x}}\:+\sqrt{\mathrm{35}+{x}}\:. \\ $$

Question Number 151677 Answers: 1 Comments: 0

Question Number 151673 Answers: 1 Comments: 0

Question Number 151665 Answers: 2 Comments: 0

prove 4arccot5−arccot239=(π/4)

$$\mathrm{prove}\:\mathrm{4arccot5}−\mathrm{arccot239}=\frac{\pi}{\mathrm{4}} \\ $$

Question Number 151721 Answers: 0 Comments: 1

Question Number 151660 Answers: 1 Comments: 0

Question Number 151652 Answers: 1 Comments: 0

faire la division de (1−x^n ) par (1−x)

$${faire}\:{la}\:{division}\:{de}\:\left(\mathrm{1}−{x}^{{n}} \right)\:{par}\:\left(\mathrm{1}−{x}\right) \\ $$

Question Number 151641 Answers: 1 Comments: 0

Question Number 151638 Answers: 1 Comments: 0

∫_( 0) ^( 2𝛑) (1 - cosx)^(10) cos(10x) dx = ?

$$\underset{\:\mathrm{0}} {\overset{\:\mathrm{2}\boldsymbol{\pi}} {\int}}\left(\mathrm{1}\:-\:\mathrm{cos}\boldsymbol{\mathrm{x}}\right)^{\mathrm{10}} \:\mathrm{cos}\left(\mathrm{10x}\right)\:\mathrm{dx}\:=\:? \\ $$

Question Number 151622 Answers: 1 Comments: 0

Find the inequality with integer coefficient for the given solution set x:x < ((−2)/5) or >(2/5)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{inequality}\:\mathrm{with}\:\mathrm{integer}\: \\ $$$$\mathrm{coefficient}\:\mathrm{for}\:\mathrm{the}\:\mathrm{given}\:\mathrm{solution}\:\mathrm{set} \\ $$$$\mathrm{x}:\mathrm{x}\:<\:\frac{−\mathrm{2}}{\mathrm{5}}\:\mathrm{or}\:>\frac{\mathrm{2}}{\mathrm{5}} \\ $$

Question Number 151616 Answers: 0 Comments: 4

let f(x)=((𝛌+x)/(1+x^2 )) and 𝛌≥((-3)/4) solve in R f(f(f(x))) ≤ 0

$$\mathrm{let}\:\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\boldsymbol{\lambda}+\mathrm{x}}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\:\mathrm{and}\:\:\boldsymbol{\lambda}\geqslant\frac{-\mathrm{3}}{\mathrm{4}} \\ $$$$\mathrm{solve}\:\mathrm{in}\:\mathbb{R}\:\:\:\mathrm{f}\left(\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\right)\:\leqslant\:\mathrm{0} \\ $$

Question Number 151615 Answers: 1 Comments: 0

How many numbers greater than 200 can be formed from the digits 1,2,3,4,5 if no digit is to be repeated in any particular number?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{numbers}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{200}\:\mathrm{can} \\ $$$$\mathrm{be}\:\mathrm{formed}\:\mathrm{from}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\:\mathrm{if}\:\mathrm{no} \\ $$$$\mathrm{digit}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{repeated}\:\mathrm{in}\:\mathrm{any}\:\mathrm{particular} \\ $$$$\mathrm{number}? \\ $$$$ \\ $$

Question Number 151614 Answers: 1 Comments: 0

𝛀 =∫_( 0) ^( 2𝛑) ((x + tan(sinx))/(𝛌 + cos(x))) dx ; 𝛌>1

$$\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\mathrm{2}\boldsymbol{\pi}} {\int}}\frac{\mathrm{x}\:+\:\mathrm{tan}\left(\mathrm{sin}\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\lambda}\:+\:\mathrm{cos}\left(\boldsymbol{\mathrm{x}}\right)}\:\mathrm{dx}\:\:;\:\:\boldsymbol{\lambda}>\mathrm{1} \\ $$

Question Number 151612 Answers: 0 Comments: 0

∫_0 ^e (x/( (√(x−ln(x)))))dx

$$\int_{\mathrm{0}} ^{{e}} \frac{{x}}{\:\sqrt{{x}−{ln}\left({x}\right)}}{dx} \\ $$

Question Number 151609 Answers: 1 Comments: 0

Question Number 151602 Answers: 6 Comments: 0

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