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Question Number 33977 Answers: 1 Comments: 0

find a polynome solution of the diifferencial equation y^(′′) +y =x^(12) .

$f i n d a p o l y n o m e s o l u t i o n o f t h e d i i f f e r e n c i a l$ $e q u a t i o n y^{^{″}} + y = x^{12} .$

Question Number 33969 Answers: 2 Comments: 0

if tanA+tanB=P and AtanB=q express the value of cos(2A+3B) in terms of p and q.

$if tanA + tanB = P and AtanB = q$ $express the value of \cos (2 A + 3 B) in terms of p and q .$

Question Number 33944 Answers: 1 Comments: 0

If the equation (p^2 −4)(p^2 −9)x^3 +[((p−2)/2)]x^2 +(p−4)(p−3)(p−2)x+{2p−1}=0. is satisfied by all values of x in (0,3] then sum of all possible integral values of ′p′ is ? {.} = fractional part function. [.]= greatest integer function.

$I f the equation$ $(p^{2} - 4) (p^{2} - 9) x^{3} + [\frac{p - 2}{2}] x^{2} + (p - 4) (p - 3) (p - 2) x + {2 p - 1} = 0 .$ $is satisfied by all values of x in (0, 3] t h e n$ $s u m o f a l l p o s s i b l e i n t e g r a l v a l u e s o f$ $^{'} p^{'} i s ?$ ${.} = f r a c t i o n a l p a r t f u n c t i o n .$ $[.] = g r e a t e s t i n t e g e r f u n c t i o n .$

Question Number 33942 Answers: 1 Comments: 1

Question Number 33941 Answers: 0 Comments: 0

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Question Number 33940 Answers: 3 Comments: 0

Let a,b are positive real numbers such that a−b=10 , then the smallest value of the constant k for which (√((x^2 +ax))) − (√((x^2 +bx))) < k for all x>0 is ?

$L e t a, b a r e p o s i t i v e r e a l n u m b e r s s u c h$ $t h a t a - b = 10, t h e n t h e s m a l l e s t v a l u e$ $o f t h e c o n s t a n t k f o r w h i c h$ $\sqrt{(x^{2} + a x)} - \sqrt{(x^{2} + b x)} < k f o r a l l x > 0$ $i s ?$

Question Number 33930 Answers: 1 Comments: 0

Three forces of magnitude 6N,2N and 3N act on the same point on the north,south and west directions respectively. find the magnitude and direction of the resultant force.

$Three forces of magnitude 6 N, 2 N$ $and 3 N act on the same point on the$ $north, south and west directions respectively .$ $find the magnitude and direction of the$ $resultant force .$

Question Number 33927 Answers: 0 Comments: 6

Question Number 33926 Answers: 0 Comments: 0

Question Number 33915 Answers: 2 Comments: 3

let Γ(x)=∫_0 ^∞ t^(x−1) e^(−t) dt with x>0 1) find Γ^((n)) (x) with n∈ N^★ 2) calculate Γ(n +(3/2)) for n integr.

$l e t Γ (x) = \int_{0}^{\infty} t^{x - 1} e^{- t} d t w i t h x > 0$ $1) f i n d Γ^{(n)} (x) w i t h n \in N^{★}$ $2) c a l c u l a t e Γ (n + \frac{3}{2}) f o r n i n t e g r .$

Question Number 33912 Answers: 0 Comments: 3

Question Number 33907 Answers: 0 Comments: 1

Question Number 33899 Answers: 2 Comments: 0

express ((4t^2 −28)/(t^4 +t^2 −6)) as a partial fraction.

$express \frac{4 t^{2} - 28}{t^{4} + t^{2} - 6} as a partial fraction .$

Question Number 33897 Answers: 2 Comments: 0

let consider ψ(x)=((Γ^′ (x))/(Γ(x))) 1) prove that ∀ a>0 ∫_0 ^1 ψ(a+x)dx=ln(a) 2) prove that ∀ n∈ N^★ ∫_0 ^1 ψ(x)sin(2πnx)dx=−(π/2)

$l e t c o n s i d e r ψ (x) = \frac{Γ^{^{'}} (x)}{Γ (x)}$ $1) p r o v e t h a t \forall a > 0 \int_{0}^{1} ψ (a + x) d x = l n (a)$ $2) p r o v e t h a t \forall n \in N^{★} \int_{0}^{1} ψ (x) s i n (2 π n x) d x = - \frac{π}{2}$

Question Number 33896 Answers: 3 Comments: 0

let Γ(x)=∫_0 ^∞ t^(x−1) e^(−t) dt 1) find Γ(x+1) interms of Γ(x) with x>0 2)calculate Γ(n) for n ∈ N^★ 3)calculate Γ((3/2)) .

$l e t Γ (x) = \int_{0}^{\infty} t^{x - 1} e^{- t} d t$ $1) f i n d Γ (x + 1) i n t e r m s o f Γ (x) w i t h x > 0$ $2) c a l c u l a t e Γ (n) f o r n \in N^{★}$ $3) c a l c u l a t e Γ (\frac{3}{2}) .$

Question Number 33895 Answers: 3 Comments: 0

let Γ(x)=∫_0 ^∞ t^(x−1) e^(−t) dt with x>0 1) prove that Γ(x)Γ(1−x)= (π/(sin(πx))) 2) find the value of ∫_0 ^∞ e^(−x^2 ) dx .

$l e t Γ (x) = \int_{0}^{\infty} t^{x - 1} e^{- t} d t w i t h x > 0$ $1) p r o v e t h a t Γ (x) Γ (1 - x) = \frac{π}{s i n (π x)}$ $2) f i n d t h e v a l u e o f \int_{0}^{\infty} e^{- x^{2}} d x .$

Question Number 33894 Answers: 0 Comments: 1

1)let f R→C 2π periodic even /f(x)=x ∀ x∈[0,π[ developp f at fourier serie 2) calculate Σ_(p=0) ^∞ (1/((2p+1)^2 )) .

$1) l e t f R \to C 2 π p e r i o d i c e v e n / f (x) = x$ $\forall x \in [0, π [d e v e l o p p f a t f o u r i e r s e r i e$ $2) c a l c u l a t e \sum_{p = 0}^{\infty} \frac{1}{{(2 p + 1)}^{2}} .$

Question Number 33892 Answers: 0 Comments: 1

prove that Σ_(n=1) ^∞ (H_n /n^2 ) =2 ξ(3) with ξ(x) =Σ_(n=1) ^∞ (1/n^x ) and x>1.

$p r o v e t h a t \sum_{n = 1}^{\infty} \frac{H_{n}}{n^{2}} = 2 ξ (3) w i t h$ $ξ (x) = \sum_{n = 1}^{\infty} \frac{1}{n^{x}} a n d x > 1 .$

Question Number 33891 Answers: 0 Comments: 1

let a∈C and ∣a∣<1 prove that the function f(x)= Σ_(n=0) ^(+∞) (a^n /(x+n)) is?developpable at point 1 and the radius is r=1.

$l e t a \in C a n d ∣ a ∣< 1 p r o v e t h a t t h e f u n c t i o n$ $f (x) = \sum_{n = 0}^{+ \infty} \frac{a^{n}}{x + n} i s ? d e v e l o p p a b l e a t p o i n t 1 a n d$ $t h e r a d i u s i s r = 1 .$

Question Number 33890 Answers: 0 Comments: 0

find lim_(x→+∞) Σ_(n=1) ^∞ (1+(1/n))^n^2 (x^n /(n!)) .

$f i n d {l i m}_{x \to + \infty} \sum_{n = 1}^{\infty} {(1 + \frac{1}{n})}^{n^{2}} \frac{x^{n}}{n!} .$

Question Number 33889 Answers: 0 Comments: 0

prove that ∫_0 ^1 (dx/(√(1−x^4 ))) = Σ_(n=0) ^∞ (C_(2n) ^n /(4^n (4n+1))) .

$p r o v e t h a t \int_{0}^{1} \frac{d x}{\sqrt{1 - x^{4}}} = \sum_{n = 0}^{\infty} \frac{C_{2 n}^{n}}{4^{n} (4 n + 1)} .$

Question Number 33888 Answers: 0 Comments: 0

developp at integr serie f(x)= ∫_0 ^(π/2) (dt/(√(1−x^2 sin^2 t))) . with ∣x∣<1 .

$d e v e l o p p a t i n t e g r s e r i e f (x) = \int_{0}^{\frac{π}{2}} \frac{d t}{\sqrt{1 - x^{2} {s i n}^{2} t}} .$ $w i t h ∣ x ∣< 1 .$

Question Number 33887 Answers: 0 Comments: 0

find the value of Σ_(n=0) ^∞ (((−1)^n )/(4n+1)) .

$f i n d t h e v a l u e o f \sum_{n = 0}^{\infty} \frac{{(- 1)}^{n}}{4 n + 1} .$

Question Number 33886 Answers: 0 Comments: 1

find the value of Σ_(n=0) ^∞ (((−1)^n )/(2n+3)).

$f i n d t h e v a l u e o f \sum_{n = 0}^{\infty} \frac{{(- 1)}^{n}}{2 n + 3} .$

Question Number 33885 Answers: 0 Comments: 1

developp at integr serie f(x)= ∫_0 ^x sin(t^2 )dt .

$d e v e l o p p a t i n t e g r s e r i e f (x) = \int_{0}^{x} s i n (t^{2}) d t .$

Question Number 33884 Answers: 0 Comments: 1

let F(x)= ∫_0 ^(π/2) ((arctan(xtant))/(tant)) dt find a simple form of f(x) . 2) find the value of ∫_0 ^(π/2) ((arctan(2tant))/(tant))dt .

$l e t F (x) = \int_{0}^{\frac{π}{2}} \frac{a r c t a n (x t a n t)}{t a n t} d t f i n d a s i m p l e$ $f o r m o f f (x) .$ $2) f i n d t h e v a l u e o f \int_{0}^{\frac{π}{2}} \frac{a r c t a n (2 t a n t)}{t a n t} d t .$

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