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Question Number 154476 Answers: 3 Comments: 0

soit:y′′−3y′−4y=3e^(3x ) avec , f(o)=−(1/2) et f′(0)=4 alors f(1)=?

$${soit}:{y}''−\mathrm{3}{y}'−\mathrm{4}{y}=\mathrm{3}{e}^{\mathrm{3}{x}\:} \:{avec}\:, \\ $$$${f}\left({o}\right)=−\frac{\mathrm{1}}{\mathrm{2}}\:{et}\:{f}'\left(\mathrm{0}\right)=\mathrm{4} \\ $$$${alors}\:{f}\left(\mathrm{1}\right)=? \\ $$$$ \\ $$

Question Number 154475 Answers: 2 Comments: 4

Question Number 154467 Answers: 1 Comments: 0

Π_(n=1) ^∞ (((1+ (1/n))^(1/2) )/(1+ (1/(2n))))

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\frac{\left(\mathrm{1}+\:\frac{\mathrm{1}}{{n}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} }{\mathrm{1}+\:\frac{\mathrm{1}}{\mathrm{2}{n}}} \\ $$$$\: \\ $$

Question Number 154465 Answers: 0 Comments: 2

Question Number 154458 Answers: 1 Comments: 0

Question Number 154456 Answers: 1 Comments: 2

S=90^2 +91^2 +.....+100^2 = ??

$${S}=\mathrm{90}^{\mathrm{2}} +\mathrm{91}^{\mathrm{2}} +.....+\mathrm{100}^{\mathrm{2}} \:\:=\:\:?? \\ $$

Question Number 154469 Answers: 1 Comments: 0

prove:∫_0 ^( 1) ln (4− 2x +x^( 2) )dx =2ln((2/e)) +(π/( (√3)))

$$ \\ $$$${prove}:\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\:\left(\mathrm{4}−\:\mathrm{2}{x}\:+{x}^{\:\mathrm{2}} \right){dx}\:=\mathrm{2}{ln}\left(\frac{\mathrm{2}}{{e}}\right)\:+\frac{\pi}{\:\sqrt{\mathrm{3}}} \\ $$$$ \\ $$

Question Number 154444 Answers: 2 Comments: 1

Question Number 154441 Answers: 1 Comments: 1

Π_(n=1) ^∞ (( (1+ (1/n))^2 )/( 1+ (2/n) ))

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\frac{\:\left(\mathrm{1}+\:\frac{\mathrm{1}}{{n}}\right)^{\mathrm{2}} \:}{\:\mathrm{1}+\:\frac{\mathrm{2}}{{n}}\:} \\ $$$$\: \\ $$

Question Number 154440 Answers: 0 Comments: 0

arcsec(sec+2)=??

$${arcsec}\left({sec}+\mathrm{2}\right)=?? \\ $$

Question Number 154437 Answers: 3 Comments: 0

∫_0 ^(π/2) arcos(((cosx)/(1+2cosx)))dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {arcos}\left(\frac{{cosx}}{\mathrm{1}+\mathrm{2}{cosx}}\right){dx} \\ $$

Question Number 154434 Answers: 1 Comments: 0

Question Number 154433 Answers: 0 Comments: 0

Question Number 154422 Answers: 0 Comments: 0

∫((a^2 sin^2 θ+b^2 cos^2 θ)/(a^4 sin^2 θ+b^4 cos^2 θ))dθ

$$\int\frac{\mathrm{a}^{\mathrm{2}} \mathrm{sin}\:^{\mathrm{2}} \theta+\mathrm{b}^{\mathrm{2}} \mathrm{cos}\:^{\mathrm{2}} \theta}{\mathrm{a}^{\mathrm{4}} \mathrm{sin}\:^{\mathrm{2}} \theta+\mathrm{b}^{\mathrm{4}} \mathrm{cos}\:^{\mathrm{2}} \theta}\mathrm{d}\theta \\ $$

Question Number 154421 Answers: 2 Comments: 0

∫[((x/e))^x +((e/x))^x ]ln xdx

$$\int\left[\left(\frac{\mathrm{x}}{\mathrm{e}}\right)^{\mathrm{x}} +\left(\frac{\mathrm{e}}{\mathrm{x}}\right)^{\mathrm{x}} \right]\mathrm{ln}\:\mathrm{xdx} \\ $$

Question Number 154429 Answers: 0 Comments: 3

Question Number 154415 Answers: 1 Comments: 1

Question Number 154424 Answers: 0 Comments: 1

Question Number 154409 Answers: 1 Comments: 0

nice calculus.. prove that : I:=∫_0 ^( ∞) (( (1+e^( −x) )sin^( 2) (x))/x^( (3/2)) ) =(√(2π)) ( 1+ (√((√2) − 1)) ) m.n

$$ \\ $$$$\:\:{nice}\:{calculus}.. \\ $$$$\:\:\:\:\:{prove}\:\:{that}\:: \\ $$$$\: \\ $$$$\:\mathrm{I}:=\int_{\mathrm{0}} ^{\:\infty} \frac{\:\left(\mathrm{1}+{e}^{\:−{x}} \:\right){sin}^{\:\mathrm{2}} \left({x}\right)}{{x}^{\:\frac{\mathrm{3}}{\mathrm{2}}} }\:=\sqrt{\mathrm{2}\pi}\:\left(\:\mathrm{1}+\:\sqrt{\sqrt{\mathrm{2}}\:−\:\mathrm{1}}\:\right) \\ $$$$\:{m}.{n} \\ $$

Question Number 154407 Answers: 0 Comments: 2

How to do it by ⊂ and ⊃ ?

$${How}\:{to}\:{do}\:{it}\:{by}\:\subset\:{and}\:\supset\:? \\ $$

Question Number 154402 Answers: 0 Comments: 2

dear tinku tara: can you stop this guy who continuously misuses the forum for his own purposes, but not for exchanging with others. he doesn′t answer any request of other people in english or even in his native language. he ignores that other people red flag his posts. i don′t think people with such behavior are an enrichment for the forum. the forum is a public place. even there are no written roles, but it is clear what the forum is for. i think when we are in the cinema, we also don′t like that someone makes picnic in it.

$${dear}\:{tinku}\:{tara}: \\ $$$${can}\:{you}\:{stop}\:{this}\:{guy}\:{who}\:{continuously} \\ $$$${misuses}\:{the}\:{forum}\:{for}\:{his}\:{own} \\ $$$${purposes},\:{but}\:{not}\:{for}\:{exchanging}\:{with} \\ $$$${others}.\:{he}\:{doesn}'{t}\:{answer}\:{any}\:{request} \\ $$$${of}\:{other}\:{people}\:{in}\:{english}\:{or}\:{even}\:{in} \\ $$$${his}\:{native}\:{language}.\:{he}\:{ignores}\:{that} \\ $$$${other}\:{people}\:{red}\:{flag}\:{his}\:{posts}. \\ $$$${i}\:{don}'{t}\:{think}\:{people}\:{with}\:{such}\:{behavior} \\ $$$${are}\:{an}\:{enrichment}\:{for}\:{the}\:{forum}. \\ $$$${the}\:{forum}\:{is}\:{a}\:{public}\:{place}.\:{even}\:{there} \\ $$$${are}\:{no}\:{written}\:{roles},\:{but}\:{it}\:{is}\:{clear} \\ $$$${what}\:{the}\:{forum}\:{is}\:{for}.\:{i}\:{think}\:{when} \\ $$$${we}\:{are}\:{in}\:{the}\:{cinema},\:{we}\:{also}\:{don}'{t} \\ $$$${like}\:{that}\:{someone}\:{makes}\:{picnic}\:{in}\:{it}. \\ $$

Question Number 154401 Answers: 3 Comments: 0

prove that the sum 2+2^2 +2^3 +2^4 +...+2^(2019) +2^(2020) is divisible by 30

$$\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum} \\ $$$$\mathrm{2}+\mathrm{2}^{\mathrm{2}} +\mathrm{2}^{\mathrm{3}} +\mathrm{2}^{\mathrm{4}} +...+\mathrm{2}^{\mathrm{2019}} +\mathrm{2}^{\mathrm{2020}} \\ $$$$\mathrm{is}\:\mathrm{divisible}\:\:\mathrm{by}\:\:\mathrm{30} \\ $$

Question Number 154400 Answers: 1 Comments: 0

x(√y) - y(√x) = 82 x(√x) + y(√y) = 83 (9/5) ∙ (x + y) = ?

$$\mathrm{x}\sqrt{\mathrm{y}}\:-\:\mathrm{y}\sqrt{\mathrm{x}}\:=\:\mathrm{82} \\ $$$$\mathrm{x}\sqrt{\mathrm{x}}\:+\:\mathrm{y}\sqrt{\mathrm{y}}\:=\:\mathrm{83} \\ $$$$\frac{\mathrm{9}}{\mathrm{5}}\:\centerdot\:\left(\mathrm{x}\:+\:\mathrm{y}\right)\:=\:? \\ $$

Question Number 154398 Answers: 1 Comments: 0

Question Number 154395 Answers: 1 Comments: 1

Question Number 154396 Answers: 1 Comments: 0

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