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Question Number 140488    Answers: 0   Comments: 2

Question Number 140487    Answers: 0   Comments: 0

∫_0 ^∞ ((1/( (√(1+x))))−(1/( (√(1+x^2 )))))(dx/x)=log(2)

0(11+x11+x2)dxx=log(2)

Question Number 140481    Answers: 0   Comments: 0

Question Number 140475    Answers: 0   Comments: 0

∫_0 ^( (π/2)) ((tan^(−1) ((√(tanx))))/(tanx))dx how can solve this

0π2tan1(tanx)tanxdxhowcansolvethis

Question Number 140474    Answers: 1   Comments: 0

Question Number 140447    Answers: 1   Comments: 0

Question Number 140446    Answers: 0   Comments: 0

If the area of a triangle with vertices Z_1 , Z_2 and Z_3 is the absolute value of the number λi determinant ((Z_1 ,Z_1 ^ ,1),(Z_2 ,Z_2 ^ ,1),(Z_3 ,Z_3 ^ ,1)) then the value of 1/λ is equal to _____.

IftheareaofatrianglewithverticesZ1,Z2andZ3istheabsolutevalueofthenumberλi|Z1Z¯11Z2Z¯21Z3Z¯31|thenthevalueof1/λisequalto_____.

Question Number 140445    Answers: 0   Comments: 0

If the straight lines a_i ^ z+a_i z^ +b_i =0(i=1, 2, 3), where b_i are real, are concurrent, then Σb_i (a_2 a_3 ^ −a_2 ^ a_3 ) is equal to _____.

Ifthestraightlinesa¯iz+aiz¯+bi=0(i=1,2,3),wherebiarereal,areconcurrent,thenΣbi(a2a¯3a¯2a3)isequalto_____.

Question Number 140444    Answers: 1   Comments: 0

If the points 1+2i and −1+4i are reflections of each other in the line z(1+i)+z^ (1−i)+K=0, then the value of K is _____.

Ifthepoints1+2iand1+4iarereflectionsofeachotherinthelinez(1+i)+z¯(1i)+K=0,thenthevalueofKis_____.

Question Number 140443    Answers: 1   Comments: 0

If z_2 /z_1 is purely imaginary and a and b are non-zero real numbers, then ∣(az_1 +bz_2 )/(az_1 −bz_2 )∣ is equal to _____.

Ifz2/z1ispurelyimaginaryandaandbarenonzerorealnumbers,then(az1+bz2)/(az1bz2)isequalto_____.

Question Number 140442    Answers: 1   Comments: 0

If z_1 and z_2 are complex numbers such that ∣z_2 ∣≠1 and ∣(z_1 −2z_2 )/(2−z_1 z_2 ^ )∣=1, then ∣z_1 ∣ is equal to _____.

Ifz1andz2arecomplexnumberssuchthatz2∣≠1and(z12z2)/(2z1z¯2)∣=1,thenz1isequalto_____.

Question Number 140428    Answers: 1   Comments: 1

If 4x=3(Mod 6), find the first four values of x.

If4x=3(Mod6),findthefirstfourvaluesofx.

Question Number 140477    Answers: 3   Comments: 0

If sin θ+sin^2 θ+sin^3 θ+.... = cos θ and 0<θ<(π/2) then find θ.

Ifsinθ+sin2θ+sin3θ+....=cosθand0<θ<π2thenfindθ.

Question Number 140424    Answers: 0   Comments: 0

Question Number 140494    Answers: 1   Comments: 0

tan^(−1) (((1−x)/(1+x)))+cot^(−1) (((1+x)/(1−x)))= (π/2) x=?

tan1(1x1+x)+cot1(1+x1x)=π2x=?

Question Number 140417    Answers: 1   Comments: 0

if minimum value of g(a;b)=(√(a^2 +b^2 −10a−10b+50))+(√(b^2 −4y+20))+ +(√(a^2 −14a+74)) is n and occurs at a=γ , b=δ, the find (n+4γ+3δ)=?

ifminimumvalueofg(a;b)=a2+b210a10b+50+b24y+20++a214a+74isnandoccursata=γ,b=δ,thefind(n+4γ+3δ)=?

Question Number 140407    Answers: 0   Comments: 0

prove that ⟨ X:=R , τ_e ⟩ is a second topology space . τ_e is Euclidian topology on R. Hint :: B= { (r−(1/n) ,r+(1/n))∣ r∈Q , n∈N} is a base for τ_(e ) .....

provethatX:=R,τeisasecondtopologyspace.τeisEuclidiantopologyonR.Hint::B={(r1n,r+1n)rQ,nN}isabaseforτe.....

Question Number 140405    Answers: 1   Comments: 0

find the value of :: Θ :=Σ_(n=1 ) ^∞ (1/(4n.(4n+1).(4n+2).(4n+3)))=?

findthevalueof::Θ:=n=114n.(4n+1).(4n+2).(4n+3)=?

Question Number 140401    Answers: 2   Comments: 0

evaluate :: Φ:=∫_0 ^( ∞) xe^(−(x^2 /4)) ln(x)dx = m.( π γ) find ” m ” ......

evaluate::Φ:=0xex24ln(x)dx=m.(πγ)findm......

Question Number 140399    Answers: 1   Comments: 0

𝛏 :=∫_0 ^( ∞) ((e^(−x^2 ) −e^(−x) )/x) dx = k.γ find ” k ” ... γ := Euler constant....

ξ:=0ex2exxdx=k.γfindk...γ:=Eulerconstant....

Question Number 140395    Answers: 0   Comments: 0

Q135933

Q135933

Question Number 140392    Answers: 0   Comments: 0

let f:[0;1]→R, prove that ∃x_0 ,x_1 ,x_2 ∈(0;1) such that ((f(x_0 ))/x_0 ^2 )+((f(x_1 ))/(2x_1 ^2 ))=3f(x_2 )

letf:[0;1]R,provethatx0,x1,x2(0;1)suchthatf(x0)x02+f(x1)2x12=3f(x2)

Question Number 140388    Answers: 3   Comments: 0

∫_0 ^∞ ((ln x)/((x^2 +a^2 )^5 )) dx

0lnx(x2+a2)5dx

Question Number 140387    Answers: 1   Comments: 0

Question Number 140430    Answers: 0   Comments: 0

(1+2x)(x^2 +1)(x^4 +x^3 −2x^2 +5x+1)^2 ={(x^3 −2x^2 +x+1)(x+1)(x^2 +1) −x^2 (1+2x)(x+3)}^2 Any good non-zero real solution to this equation in the exact form with the help of a calculator, perhaps...(please help)

(1+2x)(x2+1)(x4+x32x2+5x+1)2={(x32x2+x+1)(x+1)(x2+1)x2(1+2x)(x+3)}2Anygoodnonzerorealsolutiontothisequationintheexactformwiththehelpofacalculator,perhaps...(pleasehelp)

Question Number 140384    Answers: 1   Comments: 0

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