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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

Question Number 154390    Answers: 1   Comments: 1

lim_(x→2) ((x^2 e^x −4e^2 )/(x−2)) ?

$$\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} {e}^{{x}} −\mathrm{4}{e}^{\mathrm{2}} }{{x}−\mathrm{2}}\:? \\ $$

Question Number 154385    Answers: 2   Comments: 0

if (x)^(1/3) −((x−36))^(1/3) =3 find x−(1/x)

$${if}\:\:\:\sqrt[{\mathrm{3}}]{{x}}−\sqrt[{\mathrm{3}}]{{x}−\mathrm{36}}=\mathrm{3}\:\:\:\:\:\:{find}\:\:\:\:{x}−\frac{\mathrm{1}}{{x}} \\ $$

Question Number 154383    Answers: 0   Comments: 0

Question Number 154384    Answers: 1   Comments: 0

If x;y;z>0 then: ((4x^2 )/(x+y)) + ((8y^2 )/(y+z)) + ((4z^2 )/(z+x)) ≥ 2x + 5y + z

$$\mathrm{If}\:\:\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:\:\mathrm{then}: \\ $$$$\frac{\mathrm{4x}^{\mathrm{2}} }{\mathrm{x}+\mathrm{y}}\:+\:\frac{\mathrm{8y}^{\mathrm{2}} }{\mathrm{y}+\mathrm{z}}\:+\:\frac{\mathrm{4z}^{\mathrm{2}} }{\mathrm{z}+\mathrm{x}}\:\geqslant\:\mathrm{2x}\:+\:\mathrm{5y}\:+\:\mathrm{z} \\ $$

Question Number 154380    Answers: 1   Comments: 0

Question Number 154372    Answers: 0   Comments: 0

If a;b;c>0 and a^2 +b^2 +c^2 =3 Then prove that: Σ (a^3 /(b^2 + b + bc)) ≥ 1

$$\mathrm{If}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} =\mathrm{3} \\ $$$$\mathrm{Then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\Sigma\:\frac{\mathrm{a}^{\mathrm{3}} }{\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{b}\:+\:\mathrm{bc}}\:\geqslant\:\mathrm{1} \\ $$

Question Number 154368    Answers: 0   Comments: 0

Question Number 154365    Answers: 0   Comments: 0

Question Number 154359    Answers: 1   Comments: 0

If f(0)=1, f(2)=3, f ′(2)=5, find the value of ∫_0 ^( 1) x f′′(2x) dx.

$$\mathrm{If}\:{f}\left(\mathrm{0}\right)=\mathrm{1},\:{f}\left(\mathrm{2}\right)=\mathrm{3},\:{f}\:'\left(\mathrm{2}\right)=\mathrm{5}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}\:{f}''\left(\mathrm{2}{x}\right)\:{dx}. \\ $$

Question Number 154353    Answers: 1   Comments: 4

Question Number 154352    Answers: 0   Comments: 0

∫(x^(n−1) /(x^(3n+1) (x^n −1)))dx=?

$$\:\int\frac{{x}^{{n}−\mathrm{1}} }{{x}^{\mathrm{3}{n}+\mathrm{1}} \left({x}^{{n}} −\mathrm{1}\right)}{dx}=? \\ $$

Question Number 154351    Answers: 3   Comments: 0

∫_(−1) ^( 0) ((x−1)/( (√(x^2 −4x+3)) )) dx =?

$$\int_{−\mathrm{1}} ^{\:\mathrm{0}} \:\frac{{x}−\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{3}}\:}\:{dx}\:=? \\ $$

Question Number 154343    Answers: 1   Comments: 0

Question Number 154337    Answers: 2   Comments: 0

etudier la continuite, et derivabilite: x^2 sin((1/x)) si≠0 et f(0)=0

$${etudier}\:{la}\:{continuite},\:{et}\:{derivabilite}: \\ $$$${x}^{\mathrm{2}} {sin}\left(\frac{\mathrm{1}}{{x}}\right)\:{si}\neq\mathrm{0}\:{et}\:{f}\left(\mathrm{0}\right)=\mathrm{0} \\ $$

Question Number 154334    Answers: 3   Comments: 1

the n^(th) term of 1 , 2, 6, 24, 120 ........ is?

$${the}\:{n}^{{th}} \:{term}\:{of} \\ $$$$\mathrm{1}\:,\:\mathrm{2},\:\mathrm{6},\:\mathrm{24},\:\mathrm{120}\:........\:{is}? \\ $$

Question Number 154328    Answers: 2   Comments: 0

S=(1/(1+10))+(2/(1+10^2 ))+(4/(1+10^4 ))+(8/(1+10^8 ))+…

$$\:{S}=\frac{\mathrm{1}}{\mathrm{1}+\mathrm{10}}+\frac{\mathrm{2}}{\mathrm{1}+\mathrm{10}^{\mathrm{2}} }+\frac{\mathrm{4}}{\mathrm{1}+\mathrm{10}^{\mathrm{4}} }+\frac{\mathrm{8}}{\mathrm{1}+\mathrm{10}^{\mathrm{8}} }+\ldots\: \\ $$$$ \\ $$

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