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Question Number 61326 Answers: 0 Comments: 4

find ∫_0 ^1 ((sinx)/(1+x^2 ))dx

$f i n d \int_{0}^{1} \frac{s i n x}{1 + x^{2}} d x$

Question Number 61322 Answers: 1 Comments: 0

Question Number 61320 Answers: 1 Comments: 0

solve for x: x^4 −x=12

$solve for x :$ $x^{4} - x = 12$

Question Number 61318 Answers: 1 Comments: 0

Question Number 61313 Answers: 0 Comments: 3

how to calculate lim_(n→+∞) 0.05^(0.05^(0.05^.^.^(.0.05) ) ) }n in a simple and fast way?

$h o w t o c a l c u l a t e \underset{n \to + \infty}{\lim 0} . 05^{0 . 05^{0 . 05^{.^{.^{. 0.05}}}}}} n$ $i n a s i m p l e a n d f a s t w a y ?$

Question Number 61303 Answers: 2 Comments: 3

Question Number 61297 Answers: 0 Comments: 0

A container is 50% full of water at triple point phase . It′s Isolated and subjected to space system defining no gravity acting on the particles , Which state of matter is now more dominant , solid , liquid , or gas ? Calculate the intermolecular distances between simultaneous two distinct states of water.

$A container is 50 % full of water at triple point$ $phase . {It}^{'} s Isolated and subjected to space$ $system defining no gravity acting on the$ $particles, Which state of matter is now$ $more dominant, solid, liquid, or gas ?$ $Calculate the intermolecular distances$ $between simultaneous two distinct states$ $of water .$

Question Number 61284 Answers: 0 Comments: 0

(998^(999) × 999^(998) × 2019^(2019) ) mod (1000) = ?

$(998^{999} \times 999^{998} \times 2019^{2019}) m o d (1000) = ?$

Question Number 61283 Answers: 1 Comments: 0

(x+y)(x^2 +y^2 )(x^3 + y^3 ) = 2 (x^4 +y^4 )(x^6 +y^6 )(x^8 + y^8 ) = 4 (x^3 + y^3 )(x^5 + y^5 )(x^7 + y^7 ) = 6 (x^4 + y^4 )(x^5 + y^5 )(x^9 + y^9 )(x^(10) + y^(10) ) = ?

$(x + y) (x^{2} + y^{2}) (x^{3} + y^{3}) = 2$ $(x^{4} + y^{4}) (x^{6} + y^{6}) (x^{8} + y^{8}) = 4$ $(x^{3} + y^{3}) (x^{5} + y^{5}) (x^{7} + y^{7}) = 6$ $(x^{4} + y^{4}) (x^{5} + y^{5}) (x^{9} + y^{9}) (x^{10} + y^{10}) = ?$

Question Number 61274 Answers: 1 Comments: 0

If p , x_1 ,x_2 ,...x_i and q,y_1 ,y_2 ,...y_i form two infinite arithmetic sequences with common difference a and b respectively , then find the locus of the point ( α , β ) where α = (1/n) Σ_(i=1) ^n x_i and β= (1/n) Σ_(i=1) ^n y_(i .)

$I f p, x_{1}, x_{2}, . . . x_{i} a n d q, y_{1}, y_{2}, . . . y_{i} f o r m t w o$ $i n f i n i t e a r i t h m e t i c s e q u e n c e s w i t h c o m m o n$ $d i f f e r e n c e a a n d b r e s p e c t i v e l y,$ $t h e n f i n d t h e l o c u s o f t h e p o i n t (α, β)$ $w h e r e α = \frac{1}{n} \sum_{i = 1}^{n} x_{i} a n d β = \frac{1}{n} \sum_{i = 1}^{n} y_{i .}$

Question Number 61272 Answers: 0 Comments: 0

Question Number 61273 Answers: 2 Comments: 2

Suppose α ,β,γ,δ are real numbers such that α+β+γ+δ = α^7 +β^7 +γ^7 +δ^7 =0 Prove that α(α+β)(α+γ)(α+δ)=0

$S u p p o s e α, β, γ, δ a r e r e a l n u m b e r s$ $s u c h t h a t α + β + γ + δ = α^{7} + β^{7} + γ^{7} + δ^{7} = 0$ $P r o v e t h a t α (α + β) (α + γ) (α + δ) = 0$

Question Number 61270 Answers: 2 Comments: 0

Question Number 61269 Answers: 3 Comments: 0

Let p(x) be a quadratic polynomial such that for distinct α and β , p(α) = α and p(β) =β prove that α and β are roots of p[p(x)]−x=0 Find the remaining roots .

$L e t p (x) b e a q u a d r a t i c p o l y n o m i a l s u c h$ $t h a t f o r d i s t i n c t α a n d β,$ $p (α) = α a n d p (β) = β$ $p r o v e t h a t α a n d β a r e r o o t s o f p [p (x)] - x = 0$ $F i n d t h e r e m a i n i n g r o o t s .$

Question Number 61268 Answers: 0 Comments: 0

Let a,b,c,d,e ≥ −1 and a+b+c+d+e=5 Find the maximum and minimum value of S =(a+b)(b+c)(c+d)(d+e)(e+a)

$L e t a, b, c, d, e ⩾ - 1 a n d a + b + c + d + e = 5$ $F i n d t h e m a x i m u m a n d m i n i m u m$ $v a l u e o f S = (a + b) (b + c) (c + d) (d + e) (e + a)$

Question Number 61267 Answers: 0 Comments: 0

Question Number 61261 Answers: 1 Comments: 0

for polynomial p(x),the value of p(3) is −2.which of the following must be true about p(x)? (a)x−5 is the factor of p(x) (b)x−2is the factor of p(x) (c)x+2 is the factor of p(x) (d)the reminder when p(x) is divide d by x−3 is −2

$f o r p o l y n o m i a l p (x), t h e v a l u e o f$ $p (3) i s - 2 . w h i c h o f t h e f o l l o w i n g$ $m u s t b e t r u e a b o u t p (x) ?$ $(a) x - 5 i s t h e f a c t o r o f p (x)$ $(b) x - 2 i s t h e f a c t o r o f p (x)$ $(c) x + 2 i s t h e f a c t o r o f p (x)$ $(d) t h e r e m i n d e r w h e n p (x) i s d i v i d e$ $d b y x - 3 i s - 2$

Question Number 61258 Answers: 1 Comments: 2

Calculate, using cartesian coodinates, the following integrals: 1) ∫∫_D dxdy being D={ (x,y)∈R^2 /0≤x≤(1/2),y+x≤1,y≥0} 2) ∫∫_D x^3 ydxdy being D={(x,y)∈R^2 /0≤x≤(1/2),y+x≤1,y≥0} 3) ∫∫_D (x/y)dxdy being D={(x,y)∈R^2 /xy≤16,x≥y,x−6≤y,x≥0,y≥1} Help please!

$C a l c u l a t e, u s i n g c a r t e s i a n c o o d i n a t e s, t h e f o l l o w i n g$ $i n t e g r a l s :$ $1) \int \int_{D} d x d y b e i n g D = {(x, y) \in R^{2} / 0 ⩽ x ⩽ \frac{1}{2}, y + x ⩽ 1, y ⩾ 0}$ $2) \int \int_{D} x^{3} y d x d y b e i n g D = {(x, y) \in R^{2} / 0 ⩽ x ⩽ \frac{1}{2}, y + x ⩽ 1, y ⩾ 0}$ $3) \int \int_{D} \frac{x}{y} d x d y b e i n g D = {(x, y) \in R^{2} / x y ⩽ 16, x ⩾ y, x - 6 ⩽ y, x ⩾ 0, y ⩾ 1}$ $H e l p p l e a s e!$

Question Number 61241 Answers: 5 Comments: 0

Question Number 61240 Answers: 1 Comments: 3

∫ ((x^(2 ) − 4)/((x^2 + 4)^2 )) dx

$\int \frac{x^{2} - 4}{{(x^{2} + 4)}^{2}} dx$

Question Number 61237 Answers: 0 Comments: 0

Question Number 61235 Answers: 0 Comments: 6

Question Number 61232 Answers: 0 Comments: 3

let U_n =∫_1 ^(+∞) (([nx]−[(n−1)x])/x^3 ) dx with n≥1 1) find U_n interms of n 2) find lim_(n→+∞) U_n 3) study the serie Σ_(n=1) ^∞ U_n

$l e t U_{n} = \int_{1}^{+ \infty} \frac{[n x] - [(n - 1) x]}{x^{3}} d x w i t h n ⩾ 1$ $1) f i n d U_{n} i n t e r m s o f n$ $2) f i n d {l i m}_{n \to + \infty} U_{n}$ $3) s t u d y t h e s e r i e \sum_{n = 1}^{\infty} U_{n}$

Question Number 61229 Answers: 1 Comments: 0

let f_n (a) =∫_0 ^a x^n (√(a^2 −x^2 ))dx with a>0 1) determine a explicit form of f(a) 2) let g_n (a) =f^′ (a) give g_n (a) at form of integral and give its value 3) find the value of ∫_0 ^2 x^3 (√(4−x^2 ))dx and ∫_0 ^(√3) x^4 (√(3−x^2 ))dx

$l e t f_{n} (a) = \int_{0}^{a} x^{n} \sqrt{a^{2} - x^{2}} d x w i t h a > 0$ $1) d e t e r m i n e a e x p l i c i t f o r m o f f (a)$ $2) l e t g_{n} (a) = f^{^{'}} (a) g i v e g_{n} (a) a t f o r m o f i n t e g r a l a n d g i v e i t s$ $v a l u e$ $3) f i n d t h e v a l u e o f \int_{0}^{2} x^{3} \sqrt{4 - x^{2}} d x a n d \int_{0}^{\sqrt{3}} x^{4} \sqrt{3 - x^{2}} d x$

Question Number 61215 Answers: 2 Comments: 0

Question Number 61208 Answers: 0 Comments: 8

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