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Question Number 164628 Answers: 1 Comments: 1

60!=abc…nm000…0 m=? n=?

$60! = \underset{―}{abc \dots nm 000 \dots 0}$ $m = ? n = ?$

Question Number 164627 Answers: 1 Comments: 0

Question Number 164626 Answers: 1 Comments: 1

Question Number 164623 Answers: 1 Comments: 0

Given a, b ∈ R. Show that : [a]+[b]≤[a+b]≤[a]+[b]+1

$G i v e n a, b \in R .$ $S h o w t h a t :$ $[a] + [b] ⩽ [a + b] ⩽ [a] + [b] + 1$

Question Number 164622 Answers: 2 Comments: 0

Show that ∀ a, b ∈ R, 1. ∣∣x∣−∣y∣∣≤∣x−y∣ 2. 1+∣xy−1∣≤(1+∣x−1∣)(1+∣y−1∣).

$S h o w t h a t \forall a, b \in R,$ $1 . ∣∣ x ∣ - ∣ y ∣∣⩽∣ x - y ∣$ $2 . 1 + ∣ x y - 1 ∣⩽ (1 + ∣ x - 1 ∣) (1 + ∣ y - 1 ∣) .$

Question Number 164615 Answers: 0 Comments: 0

Question Number 164612 Answers: 3 Comments: 0

solve: 1. ∫(1/(sinx))dx 2.∫(1/(cosx))dx

$s o l v e :$ $1 . \int \frac{1}{s i n x} d x$ $2 . \int \frac{1}{c o s x} d x$

Question Number 164609 Answers: 1 Comments: 0

en posant x=t−(1/t) ∫^(+oo) _0 ((1+t^2 )/(1+t^4 ))dt

$e n p o s a n t x = t - \frac{1}{t}$ ${\int_{0}}^{+ o o} \frac{1 + t^{2}}{1 + t^{4}} d t$

Question Number 164606 Answers: 2 Comments: 0

Min f(x)= cos 2x +(√3) sin 2x −2(√3) cos x−2sin x is ...

$M i n f (x) = \cos 2 x + \sqrt{3} \sin 2 x - 2 \sqrt{3} \cos x - 2 \sin x$ $i s . . .$

Question Number 164605 Answers: 1 Comments: 0

Question Number 164600 Answers: 3 Comments: 0

Question Number 164599 Answers: 0 Comments: 1

180<θ<270 and 2sinθ−cos θ=0 faind volue of sin θ×cos θ=?

$180 < θ < 270 a n d$ $2 s i n θ - \cos θ = 0$ $f a i n d v o l u e o f$ $\sin θ \times \cos θ = ?$

Question Number 164598 Answers: 0 Comments: 0

Prove that; ∫_(−∞) ^∞ y tan x + y^3 tan x dx = undefined

$Prove that;$ $\int_{- \infty}^{\infty} y t a n x + y^{3} t a n x d x = u n d e f i n e d$

Question Number 164591 Answers: 1 Comments: 0

pour quelle valeur α la serie converge Σ_(n=2) (ln(n)+αln(n−(1/n))

$p o u r q u e l l e v a l e u r α l a s e r i e c o n v e r g e$ $\sum_{n = 2} (l n (n) + α l n (n - \frac{1}{n})$

Question Number 164590 Answers: 1 Comments: 0

∫ ((In(x^2 .e^(cos2) ))/x) dx

$\int \frac{In (x^{2} . e^{c o s 2})}{x} dx$

Question Number 164589 Answers: 0 Comments: 0

∫ A.^5 (√(x^3 )) dx

$\int A .^{5} \sqrt{x^{3}} dx$

Question Number 164588 Answers: 0 Comments: 0

soit K un corps; pour toute permutation σ de S_n , on note P(σ) sa matrice dans la base canonique de K^n . montrer que deux permutations σ_1 et σ_2 sont conjugues dans S_n si et seulement si P(σ_1 ) et P(σ_2 ) sont semblables.

$s o i t K u n c o r p s; p o u r t o u t e p e r m u t a t i o n$ $σ d e S_{n}, o n n o t e P (σ) s a m a t r i c e d a n s l a b a s e$ $c a n o n i q u e d e K^{n} .$ $m o n t r e r q u e d e u x p e r m u t a t i o n s σ_{1} e t σ_{2} s o n t$ $c o n j u g u e s d a n s S_{n} s i e t s e u l e m e n t s i$ $P (σ_{1}) e t P (σ_{2}) s o n t s e m b l a b l e s .$

Question Number 164585 Answers: 2 Comments: 0

I = ∫_0 ^( 1) (( Li_( 2) ( x ))/(1 + x)) dx = ? −−−−−−

$I = \int_{0}^{1} \frac{{Li}_{2} (x)}{1 + x} d x = ?$ $- - - - - -$

Question Number 164576 Answers: 1 Comments: 0

Question Number 164568 Answers: 2 Comments: 0

(1/( (√(2−x)))) > (1/(x−1))

$\frac{1}{\sqrt{2 - x}} > \frac{1}{x - 1}$

Question Number 164564 Answers: 0 Comments: 0

when F does not contain y explicity . Find the extremals of ∫_x_1 ^x_2 ((y′^2 )/x^2 )dx

$w h e n F d o e s n o t c o n t a i n y e x p l i c i t y . F i n d t h e e x t r e m a l s o f$ $\underset{x_{1}}{\int^{x_{2}}} \frac{y^{' 2}}{x^{2}} d x$

Question Number 164560 Answers: 2 Comments: 1

6 boys and 6 girls go to an exhibition and the cost of ticket is Rs 10.Each girl has a 10 rupees note while each boy has a 20 rupees note. They stand in a queue at the counter and the cashier does not have any money at the begining , then the number of ways of arranging the boys and girls so that no one waits for a change is A) 132 B) 264 C) 132(720)^2 D)264(720)^2

$6 boys and 6 girls go to an exhibition and the cost$ $of ticket is Rs 10 . Each girl has a 10 rupees note$ $while each boy has a 20 rupees note . They stand$ $in a queue at the counter and the cashier does$ $not have any money at the begining, then the$ $number of ways of arranging the boys and girls$ $so that no one waits for a change is$ $A) 132 B) 264 C) 132 {(720)}^{2} D) 264 {(720)}^{2}$

Question Number 164555 Answers: 2 Comments: 0

prove that ( _( k−1) ^(2k) ) =^? Σ_(r=0) ^(k−1) ( _( r) ^( k) ) (^( ) _( r+1) ^( k) ) −−−−

$p r o v e t h a t$ $Extra \left or missing \right$ $- - - -$

Question Number 164553 Answers: 3 Comments: 1

Question Number 164549 Answers: 2 Comments: 0

Question Number 164547 Answers: 1 Comments: 0

prove Ω= ∫_0 ^( ∞) (( (√x))/(( 1+x +x^( 2) )^( 3) )) dx =^? ((π(√3))/(36)) −−m.n−−

$p r o v e$ $Ω = \int_{0}^{\infty} \frac{\sqrt{x}}{{(1 + x + x^{2})}^{3}} d x \overset{?}{=} \frac{π \sqrt{3}}{36}$ $- - m . n - -$

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