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∫_0 ^∞ ((1/( (√(1+x))))−(1/( (√(1+x^2 )))))(dx/x)=log(2) |
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∫_0 ^( (π/2)) ((tan^(−1) ((√(tanx))))/(tanx))dx how can solve this |
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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 _____. |
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 _____. |
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 _____. |
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 _____. |
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 _____. |
If 4x=3(Mod 6), find the first four values of x. |
If sin θ+sin^2 θ+sin^3 θ+.... = cos θ and 0<θ<(π/2) then find θ. |
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tan^(−1) (((1−x)/(1+x)))+cot^(−1) (((1+x)/(1−x)))= (π/2) x=? |
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)=? |
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 ) ..... |
find the value of :: Θ :=Σ_(n=1 ) ^∞ (1/(4n.(4n+1).(4n+2).(4n+3)))=? |
evaluate :: Φ:=∫_0 ^( ∞) xe^(−(x^2 /4)) ln(x)dx = m.( π γ) find ” m ” ...... |
𝛏 :=∫_0 ^( ∞) ((e^(−x^2 ) −e^(−x) )/x) dx = k.γ find ” k ” ... γ := Euler constant.... |
Q135933 |
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 ) |
∫_0 ^∞ ((ln x)/((x^2 +a^2 )^5 )) dx |
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(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) |
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Pg 718 Pg 719 Pg 720 Pg 721 Pg 722 Pg 723 Pg 724 Pg 725 Pg 726 Pg 727 |