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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)

$\int_{0}^{\infty} (\frac{1}{\sqrt{1 + x}} - \frac{1}{\sqrt{1 + x^{2}}}) \frac{d x}{x} = l o g (2)$

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

$\int_{0}^{\frac{π}{2}} \frac{{t a n}^{- 1} (\sqrt{t a n x})}{t a n x} d x$ $h o w c a n s o l v e t h i s$

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 _____.

$If the area of a triangle with vertices Z_{1}, Z_{2} and Z_{3} is$ $the absolute value of the number$ $λ i | \begin{matrix} Z_{1} & {\bar{Z}}_{1} & 1 \\ Z_{2} & {\bar{Z}}_{2} & 1 \\ Z_{3} & {\bar{Z}}_{3} & 1 \end{matrix} |$ $then the value of 1 / λ is equal to_____.$

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 _____.

$If the straight lines {\bar{a}}_{i} z + a_{i} \bar{z} + b_{i} = 0 (i = 1, 2, 3), where$ $b_{i} are real, are concurrent, then Σ b_{i} (a_{2} {\bar{a}}_{3} - {\bar{a}}_{2} a_{3}) is$ $equal to_____.$

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 _____.

$If the points 1 + 2 i and - 1 + 4 i are reflections of$ $each other in the line z (1 + i) + \bar{z} (1 - i) + K = 0, then$ $the value of K is_____.$

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 _____.

$If z_{2} / z_{1} is purely imaginary and a and b are non - zero real$ $numbers, then ∣ ({a z}_{1} + {b z}_{2}) / ({a z}_{1} - {b z}_{2}) ∣ is equal to_____.$

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 _____.

$If z_{1} and z_{2} are complex numbers such that ∣ z_{2} ∣\neq 1 and$ $∣ (z_{1} - 2 z_{2}) / (2 - z_{1} {\bar{z}}_{2}) ∣= 1, then ∣ z_{1} ∣ is equal to_____.$

Question Number 140428 Answers: 1 Comments: 1

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

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

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.

$I f \sin θ + \sin^{2} θ + \sin^{3} θ + . . . .$ $= \cos θ a n d 0 < θ < \frac{π}{2} t h e n$ $f i n d θ .$

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=?

$\tan^{- 1} (\frac{1 - x}{1 + x}) + \cot^{- 1} (\frac{1 + x}{1 - x}) = \frac{π}{2}$ $x = ?$

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)=?

$i f m i n i m u m v a l u e o f$ $g (a; b) = \sqrt{a^{2} + b^{2} - 10 a - 10 b + 50} + \sqrt{b^{2} - 4 y + 20} +$ $+ \sqrt{a^{2} - 14 a + 74}$ $i s n a n d o c c u r s a t a = γ, b = δ, t h e f i n d$ $(n + 4 γ + 3 δ) = ?$

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 ) .....

$p r o v e t h a t ⟨ X := R, τ_{e} ⟩ i s$ $a s e c o n d t o p o l o g y s p a c e .$ $τ_{e} i s E u c l i d i a n t o p o l o g y o n R .$ $H i n t :: B = {(r - \frac{1}{n}, r + \frac{1}{n}) ∣ r \in Q, n \in N}$ $i s a b a s e f o r τ_{e} . . . . .$

Question Number 140405 Answers: 1 Comments: 0

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

$f i n d t h e v a l u e o f ::$ $Θ := \underset{n = 1}{\sum^{\infty}} \frac{1}{4 n . (4 n + 1) . (4 n + 2) . (4 n + 3)} = ?$

Question Number 140401 Answers: 2 Comments: 0

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

$e v a l u a t e ::$ $Φ := \int_{0}^{\infty} {x e}^{- \frac{x^{2}}{4}} l n (x) d x = m . (π γ)$ $f i n d^{″} m^{″} . . . . . .$

Question Number 140399 Answers: 1 Comments: 0

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

$ξ := \int_{0}^{\infty} \frac{e^{- x^{2}} - e^{- x}}{x} d x = k . γ$ $f i n d^{″} k^{″} . . .$ $γ := E u l e r c o n s t a n t . . . .$

Question Number 140395 Answers: 0 Comments: 0

Q135933

$Q 135933$

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 )

$l e t f : [0; 1] \to R, p r o v e t h a t \exists x_{0}, x_{1}, x_{2} \in (0; 1)$ $s u c h t h a t \frac{f (x_{0})}{x_{0}^{2}} + \frac{f (x_{1})}{2 x_{1}^{2}} = 3 f (x_{2})$

Question Number 140388 Answers: 3 Comments: 0

∫_0 ^∞ ((ln x)/((x^2 +a^2 )^5 )) dx

$\int_{0}^{\infty} \frac{\ln x}{{(x^{2} + a^{2})}^{5}} dx$

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)

$(1 + 2 x) (x^{2} + 1) {(x^{4} + x^{3} - 2 x^{2} + 5 x + 1)}^{2}$ $= {(x^{3} - 2 x^{2} + x + 1) (x + 1) (x^{2} + 1)$ ${- x^{2} (1 + 2 x) (x + 3)}}^{2}$ $A n y g o o d n o n - z e r o r e a l s o l u t i o n$ $t o t h i s e q u a t i o n i n t h e e x a c t f o r m$ $w i t h t h e h e l p o f a c a l c u l a t o r,$ $p e r h a p s . . . (p l e a s e h e l p)$

Question Number 140384 Answers: 1 Comments: 0

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