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Question Number 27345 Answers: 0 Comments: 1

prove that ∫_0 ^∞ (t^(x−1) /(e^t −1))dt =ξ(x)Γ(x) with ξ(x)= Σ_(n=1) ^∝ (1/n^x ) and Γ(x)=∫_0 ^∞ t^(x−1) e^(−t) dt ( x>1)

$p r o v e t h a t \int_{0}^{\infty} \frac{t^{x - 1}}{e^{t} - 1} d t = ξ (x) Γ (x)$ $w i t h ξ (x) = \sum_{n = 1}^{\propto} \frac{1}{n^{x}} a n d Γ (x) = \int_{0}^{\infty} t^{x - 1} e^{- t} d t$ $(x > 1)$

Question Number 27343 Answers: 1 Comments: 7

let give A=(_(2 2) ^(1 2) ) find A^n and e^A and e^(tA) . we remind that e^A = Σ_ (A^n /(n!))

$l e t g i v e A = (_{2 2}^{1 2}) f i n d A^{n} a n d e^{A}$ $a n d e^{t A} . w e r e m i n d t h a t e^{A} = \sum_{} \frac{A^{n}}{n!}$

Question Number 27342 Answers: 0 Comments: 1

find f(x)= ∫_0 ^∞ (e^(−x(1+t^2 )) /(1+t^2 )) dt interms ofx with x≥0 and calculate ∫_0 ^∞ e^(−t^2 ) dt .

$f i n d f (x) = \int_{0}^{\infty} \frac{e^{- x (1 + t^{2})}}{1 + t^{2}} d t i n t e r m s o f x$ $w i t h x ⩾ 0 a n d c a l c u l a t e \int_{0}^{\infty} e^{- t^{2}} d t .$

Question Number 27341 Answers: 0 Comments: 0

prove that ∫_0 ^∞ e^(−(t^2 +(1/t^2 ))) dt is convergeny and find its value .

$p r o v e t h a t \int_{0}^{\infty} e^{- (t^{2} + \frac{1}{t^{2}})} d t i s c o n v e r g e n y$ $a n d f i n d i t s v a l u e .$

Question Number 27335 Answers: 0 Comments: 1

if 2 chords of ellipse have the same distance from the centre of ellipse and the eccentric angle of the end points of the chords are respectivly α β γ δ then prove that tan (α/2)×tan (β/2)×tan (γ/2)×tan (δ/2)=1

$i f 2 c h o r d s o f e l l i p s e h a v e t h e s a m e$ $d i s t a n c e f r o m t h e c e n t r e o f e l l i p s e$ $a n d t h e e c c e n t r i c a n g l e o f t h e e n d p o i n t s o f t h e c h o r d s$ $a r e r e s p e c t i v l y α β γ δ t h e n p r o v e t h a t$ $\tan \frac{α}{2} \times \tan \frac{β}{2} \times \tan \frac{γ}{2} \times \tan \frac{δ}{2} = 1$

Question Number 27334 Answers: 1 Comments: 0

(q_1 /q_2 )=((x/(0.8−x)))^2 ; x=?

$\frac{q_{1}}{q_{2}} = {(\frac{x}{0.8 - x})}^{2}; x = ?$

Question Number 27332 Answers: 1 Comments: 1

Question Number 27328 Answers: 0 Comments: 1

Question Number 27327 Answers: 0 Comments: 4

lim_(n→∞) (x^(2n) /(1+∣x∣+x^(4n) ))

$\lim_{n \to \infty} \frac{x^{2 n}}{1 + ∣ x ∣ + x^{4 n}}$

Question Number 27326 Answers: 1 Comments: 0

What is the relationship between the centre of gravity and the centre of mass?

$W h a t i s t h e r e l a t i o n s h i p b e t w e e n$ $t h e c e n t r e o f g r a v i t y a n d t h e c e n t r e o f$ $m a s s ?$

Question Number 27321 Answers: 1 Comments: 1

Question Number 27751 Answers: 0 Comments: 0

what is relation between in tensity of diffraction anx slit width

$w h a t i s r e l a t i o n b e t w e e n i n$ $t e n s i t y o f d i f f r a c t i o n a n x$ $s l i t w i d t h$

Question Number 27309 Answers: 1 Comments: 0

find the value of ∫_0 ^∝ (((−1)^([x]) )/((2x+1)^2 ))dx

$f i n d t h e v a l u e o f \int_{0}^{\propto} \frac{{(- 1)}^{[x]}}{{(2 x + 1)}^{2}} d x$

Question Number 27303 Answers: 1 Comments: 0

Question Number 27300 Answers: 3 Comments: 1

Question Number 27296 Answers: 1 Comments: 1

((sin^2 3A)/(sin^2 A)) − ((cos^2 3A)/(cos^2 A)) =

$\frac{\sin^{2} 3 A}{\sin^{2} A} - \frac{\cos^{2} 3 A}{\cos^{2} A} =$

Question Number 27295 Answers: 0 Comments: 1

The value of the integral ∫_( 0) ^π (1/(a^2 −2a cos x+1)) dx (a< 1) is

$The value of the integral$ $\underset{0}{\int^{π}} \frac{1}{a^{2} - 2 a \cos x + 1} d x (a < 1) is$

Question Number 27294 Answers: 0 Comments: 1

∫_(1/e) ^(tan x) (t/(1+t^2 )) dt + ∫_(1/e) ^(cot x) (1/(t(1+t^2 ))) dt =

$\underset{1 / e}{\int^{\tan x}} \frac{t}{1 + t^{2}} d t + \underset{1 / e}{\int^{\cot x}} \frac{1}{t (1 + t^{2})} d t =$

Question Number 27293 Answers: 1 Comments: 0

L^(−1) ((s^3 /(s^4 +4)))=?

$L^{- 1} (\frac{s^{3}}{s^{4} + 4}) = ?$

Question Number 27287 Answers: 0 Comments: 1

Question Number 27283 Answers: 0 Comments: 0

Question Number 27282 Answers: 0 Comments: 1

∫log(2+x^2 )dx

$\int l o g (2 + x^{2}) d x$

Question Number 27281 Answers: 1 Comments: 1

∫_(−1) ^1 (x^2 +cos x) log (((2+x)/(2−x)))dx = 0

$\underset{- 1}{\int^{1}} (x^{2} + \cos x) \log (\frac{2 + x}{2 - x}) d x = 0$

Question Number 27280 Answers: 1 Comments: 1

If for a real number y, [y] is the greatest integer less than or equal to y, then the value of the integeral ∫_(π/2) ^(3π/2) [2 sin x]dx is

$If for a real number y, [y] is the greatest$ $integer less than or equal to y, then the$ $value of the integeral \underset{π / 2}{\int^{3 π / 2}} [2 \sin x] d x is$

Question Number 27274 Answers: 0 Comments: 0

Question Number 27271 Answers: 1 Comments: 0

Proof ∫(1/(a^2 −x^2 ))dx =(1/(2a))ln∣((a+x)/(a−x))∣+c

$P r o o f$ $\int \frac{1}{a^{2} - x^{2}} d x = \frac{1}{2 a} l n ∣ \frac{a + x}{a - x} ∣ + c$

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