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Question Number 57923 Answers: 0 Comments: 3

decompose the fraction F(x) =(x^n /(x^(2n) −1)) inside C(x) and R(x)

$d e c o m p o s e t h e f r a c t i o n F (x) = \frac{x^{n}}{x^{2 n} - 1} i n s i d e C (x) a n d R (x)$

Question Number 57922 Answers: 0 Comments: 2

decompose inside C(x) the fraction F(x) =(1/((x^2 +1)^n )) with n integr natural and n≥1

$d e c o m p o s e i n s i d e C (x) t h e f r a c t i o n F (x) = \frac{1}{{(x^{2} + 1)}^{n}} w i t h n i n t e g r n a t u r a l$ $a n d n ⩾ 1$

Question Number 57915 Answers: 2 Comments: 0

Question Number 57914 Answers: 0 Comments: 0

Question Number 57909 Answers: 2 Comments: 0

n men and n women should be arranged alternately in a row, how many ways can this be done? if the same should be done on a table, how many ways then?

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

Question Number 57902 Answers: 1 Comments: 1

prove that the equation Z^n =1 have exacly n roots given by Z_k =e^(i((2kπ)/n)) k∈[[0,n−1]]

$p r o v e t h a t t h e e q u a t i o n Z^{n} = 1 h a v e e x a c l y n r o o t s g i v e n b y$ $Z_{k} = e^{i \frac{2 k π}{n}} k \in [[0, n - 1]]$

Question Number 57900 Answers: 0 Comments: 1

let f(x) =∫_0 ^∞ ((cos(πxt))/((t^2 +3x^2 )^2 )) dt with x>0 1) find a explicit form for f(x) 2) find the value of ∫_0 ^∞ ((cos(πt))/((t^2 +3)^2 ))dt 3) let U_n =f(n) find nature of Σ U_n

$l e t f (x) = \int_{0}^{\infty} \frac{c o s (π x t)}{{(t^{2} + 3 x^{2})}^{2}} d t w i t h x > 0$ $1) f i n d a e x p l i c i t f o r m f o r f (x)$ $2) f i n d t h e v a l u e o f \int_{0}^{\infty} \frac{c o s (π t)}{{(t^{2} + 3)}^{2}} d t$ $3) l e t U_{n} = f (n) f i n d n a t u r e o f Σ U_{n}$

Question Number 57899 Answers: 0 Comments: 2

let f(x) =∫_0 ^(+∞) (dt/((t^2 +x^2 )^3 )) with x>0 1) find a explicit form off (x) 1) calculate ∫_0 ^∞ (dx/((t^2 +3)^3 )) and ∫_0 ^∞ (dt/((t^2 +4)^3 )) 2) find the value of A(θ) =∫_0 ^∞ (dt/((t^2 +sin^2 θ)^3 )) with 0<θ<π.

$l e t f (x) = \int_{0}^{+ \infty} \frac{d t}{{(t^{2} + x^{2})}^{3}} w i t h x > 0$ $1) f i n d a e x p l i c i t f o r m o f f (x)$ $1) c a l c u l a t e \int_{0}^{\infty} \frac{d x}{{(t^{2} + 3)}^{3}} a n d \int_{0}^{\infty} \frac{d t}{{(t^{2} + 4)}^{3}}$ $2) f i n d t h e v a l u e o f A (θ) = \int_{0}^{\infty} \frac{d t}{{(t^{2} + {s i n}^{2} θ)}^{3}} w i t h 0 < θ < π .$

Question Number 57889 Answers: 0 Comments: 0

Question Number 57882 Answers: 1 Comments: 1

2[3×4+2×4]

$2 [3 \times 4 + 2 \times 4]$

Question Number 57881 Answers: 0 Comments: 0

calculate(2/(13))×2(1/4)

$calculate \frac{2}{13} \times 2 \frac{1}{4}$

Question Number 57880 Answers: 0 Comments: 0

6×2

$6 \times 2$

Question Number 57873 Answers: 1 Comments: 1

If α + β+ γ =180°, show that cos (α/2) + cos (β/2)+ cos (γ/2) = 4 cos ((β + γ)/4) cos ((γ + α)/4) cos ((α + β)/4).

$If α + β + γ = 180 °, show that \cos \frac{α}{2} + \cos \frac{β}{2} + \cos \frac{γ}{2} = 4 \cos \frac{β + γ}{4} \cos \frac{γ + α}{4} \cos \frac{α + β}{4} .$

Question Number 57866 Answers: 2 Comments: 0

lim_(n→∞) ((3^(n+2) −2.5^(n+1) )/(3^n −2.5^(n−1) ))

$\underset{n \to \infty}{l i m} \frac{3^{n + 2} - 2 . 5^{n + 1}}{3^{n} - 2 . 5^{n - 1}}$

Question Number 57865 Answers: 2 Comments: 0

Question Number 57863 Answers: 1 Comments: 2

Question Number 57864 Answers: 1 Comments: 0

Question Number 58001 Answers: 1 Comments: 1

Question Number 57850 Answers: 1 Comments: 0

lim_(n→∞) (8^n /(2^(n+1) +3^(n+2) ))

$\underset{n \to \infty}{l i m} \frac{8^{n}}{2^{n + 1} + 3^{n + 2}}$

Question Number 57848 Answers: 0 Comments: 2

1)prove that arctan(a) +arctanb =arctan(((a+b)/(1−ab))) with ab≠1 2)find the value of S_N = Σ_(n=1) ^N (−1)^n arctan(((2n+1)/(n^2 +n−1)))

$1) p r o v e t h a t a r c t a n (a) + a r c t a n b = a r c t a n (\frac{a + b}{1 - a b})$ $w i t h a b \neq 1$ $2) f i n d t h e v a l u e o f S_{N} = \sum_{n = 1}^{N} {(- 1)}^{n} a r c t a n (\frac{2 n + 1}{n^{2} + n - 1})$

Question Number 57847 Answers: 0 Comments: 1

(U_n ) is a sequence wich verify u_n +u_(n+1) =(1/n^2 ) 1) find u_n interms of n 2) find lim_(n→+∞) u_n

$(U_{n}) i s a s e q u e n c e w i c h v e r i f y$ $u_{n} + u_{n + 1} = \frac{1}{n^{2}}$ $1) f i n d u_{n} i n t e r m s o f n$ $2) f i n d {l i m}_{n \to + \infty} u_{n}$

Question Number 57840 Answers: 0 Comments: 0

A uniform rod ABC, weight 50N and length 4m rests with one end A on rough horizontal ground and is supported by a smooth peg at B where AB=2.5m. The peg is 2m from the ground. Find the reactions at A and at the peg.

$A uniform rod ABC, weight 50 N and$ $length 4 m rests with one end A on rough$ $horizontal ground and is supported by$ $a smooth peg at B where AB = 2 . 5 m .$ $The peg is 2 m from the ground . Find the$ $reactions at A and at the peg .$

Question Number 57839 Answers: 0 Comments: 0

A uniform rod AB, 3m long and weght 120N, rests in equilibrium with end A on a rough horizontal table and supported by a force P applied at its end B at right angles to the rod. The rod makes an angle of 3o° with the table. Find the force P, and the reaction at the floor.

$A uniform rod AB, 3 m long and weght$ $120 N, rests in equilibrium with end A$ $on a rough horizontal table and supported$ $by a force P applied at its end B at right$ $angles to the rod . The rod makes an angle$ $of 3 o ° with the table . Find the force P,$ $and the reaction at the floor .$

Question Number 57825 Answers: 1 Comments: 1

calculate ∫_0 ^π ((2xsinx)/(3 +cos(2x)))dx .

$c a l c u l a t e \int_{0}^{π} \frac{2 x s i n x}{3 + c o s (2 x)} d x .$

Question Number 57822 Answers: 0 Comments: 1

If A and B are two non empty equivalent sets, then a possible value of n(A×B) is

$If A and B are two non empty$ $equivalent sets, then a possible value$ $of n (A \times B) is$

Question Number 57821 Answers: 2 Comments: 0

find the common area of: { (((x^2 /3)+y^2 =1)),((x^2 +(y^2 /3)=1)) :}

$find the common area of :$ ${\begin{cases} \frac{x^{2}}{3} + y^{2} = 1 \\ x^{2} + \frac{y^{2}}{3} = 1 \end{cases}$

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