Question and Answers Forum

AllQuestion and Answers: Page 1427

Question Number 62869 Answers: 1 Comments: 0

y(dy/dx) − (y/(dy/dx)) = 2a a is a real number

$y \frac{d y}{d x} - \frac{y}{\frac{d y}{d x}} = 2 a$ $a i s a r e a l n u m b e r$

Question Number 62856 Answers: 0 Comments: 3

let f(λ) =∫_0 ^(+∞) (x^4 /(x^6 +λ^6 )) dx with λ>0 1) calculate f(λ) 2) calculate also g(λ) =∫_0 ^∞ (x^4 /((x^6 +λ^6 )^2 ))dx 3) find the values of ∫_0 ^∞ (x^4 /(x^6 +1)) dx , ∫_0 ^∞ (x^4 /(x^6 +8))dx and ∫_0 ^∞ (x^4 /((x^6 +8)^2 ))dx.

$l e t f (λ) = \int_{0}^{+ \infty} \frac{x^{4}}{x^{6} + λ^{6}} d x w i t h λ > 0$ $1) c a l c u l a t e f (λ)$ $2) c a l c u l a t e a l s o g (λ) = \int_{0}^{\infty} \frac{x^{4}}{{(x^{6} + λ^{6})}^{2}} d x$ $3) f i n d t h e v a l u e s o f \int_{0}^{\infty} \frac{x^{4}}{x^{6} + 1} d x, \int_{0}^{\infty} \frac{x^{4}}{x^{6} + 8} d x a n d \int_{0}^{\infty} \frac{x^{4}}{{(x^{6} + 8)}^{2}} d x .$

Question Number 62855 Answers: 0 Comments: 1

find ∫ ((x^4 /(1+x^6 )))^2 dx 2) calculate ∫_0 ^1 (x^8 /((1+x^6 )^2 ))dx 3) calculate ∫_0 ^(+∞) (x^8 /((1+x^6 )^2 ))dx .

$f i n d \int {(\frac{x^{4}}{1 + x^{6}})}^{2} d x$ $2) c a l c u l a t e \int_{0}^{1} \frac{x^{8}}{{(1 + x^{6})}^{2}} d x$ $3) c a l c u l a t e \int_{0}^{+ \infty} \frac{x^{8}}{{(1 + x^{6})}^{2}} d x .$

Question Number 62850 Answers: 1 Comments: 1

Question Number 62844 Answers: 1 Comments: 0

Let p(x) = ax^2 + bx + c be such that p(x) takes real values for real values of x and non−real values for non−real values of x . Prove that a = 0 and find all possible values of c.

$L e t p (x) = {a x}^{2} + b x + c b e s u c h t h a t p (x) t a k e s r e a l v a l u e s$ $f o r r e a l v a l u e s o f x a n d n o n - r e a l v a l u e s f o r n o n - r e a l$ $v a l u e s o f x . P r o v e t h a t a = 0 a n d f i n d a l l$ $p o s s i b l e v a l u e s o f c .$

Question Number 62839 Answers: 1 Comments: 3

Question Number 62836 Answers: 0 Comments: 0

Question Number 62833 Answers: 0 Comments: 2

∫((cos(x))/x) dx ∫(√(sin(x) )) dx ∫(√(1−k^2 sin^2 (x))) dx k:constant

$\int \frac{c o s (x)}{x} d x$ $\int \sqrt{s i n (x)} d x$ $\int \sqrt{1 - k^{2} {s i n}^{2} (x)} d x k : c o n s t a n t$

Question Number 62828 Answers: 0 Comments: 1

let U_n =∫_0 ^(+∞) ((cos(ch(nx)))/((3+x^2 )^2 ))dx 1) calculate U_n interms of n 2) find lim_(n→+∞) n U_n and lim_(n→+∞) n^2 U_n 3)study the serie Σ U_n

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

Question Number 62826 Answers: 0 Comments: 4

Question Number 62821 Answers: 2 Comments: 1

Question Number 62815 Answers: 0 Comments: 2

developp at fourier serie f(x) =cos(tx) ,2π periodic even .

$d e v e l o p p a t f o u r i e r s e r i e f (x) = c o s (t x), 2 π p e r i o d i c e v e n .$

Question Number 62814 Answers: 0 Comments: 10

Question Number 62813 Answers: 0 Comments: 0

find the value of ∫_0 ^∞ e^(−(t^2 +(1/t^2 ))) dt study first the convergence .

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

Question Number 62812 Answers: 0 Comments: 1

let U_n =∫_0 ^(+∞) ((arctan(nt))/(1+n^2 t^2 ))dt with n natural≥1 1) calculate U_n 2) calculate lim_(n→+∞) n^2 U_n 3) study the convergence of Σ U_n

$l e t U_{n} = \int_{0}^{+ \infty} \frac{a r c t a n (n t)}{1 + n^{2} t^{2}} d t w i t h n n a t u r a l ⩾ 1$ $1) c a l c u l a t e U_{n}$ $2) c a l c u l a t e {l i m}_{n \to + \infty} n^{2} U_{n}$ $3) s t u d y t h e c o n v e r g e n c e o f Σ U_{n}$

Question Number 62811 Answers: 0 Comments: 2

1) find ∫ ((2x^2 −1)/((x+1)(x−3)(x^2 −x+2)))dx 2)calculate ∫_5 ^(+∞) ((2x^2 −1)/((x+1)(x−3)(x^2 −x+2)))dx

$1) f i n d \int \frac{2 x^{2} - 1}{(x + 1) (x - 3) (x^{2} - x + 2)} d x$ $2) c a l c u l a t e \int_{5}^{+ \infty} \frac{2 x^{2} - 1}{(x + 1) (x - 3) (x^{2} - x + 2)} d x$

Question Number 62809 Answers: 0 Comments: 1

let f(x) = arctan(nx) with n integr natural 1) calculate f^((n)) (x) and f^((n)) (0) 2) developp f at integr serie .

$l e t f (x) = a r c t a n (n x) w i t h n i n t e g r n a t u r a l$ $1) c a l c u l a t e f^{(n)} (x) a n d f^{(n)} (0)$ $2) d e v e l o p p f a t i n t e g r s e r i e .$

Question Number 62808 Answers: 0 Comments: 0

f(t) =∫_0 ^(+∞) (e^(−xt) /((x+t)^2 ))dx with t≥0 1) study the set of definition for f(t) 2)study the continuity of f 3)study the derivability of f 4) developp f at integr serie

$f (t) = \int_{0}^{+ \infty} \frac{e^{- x t}}{{(x + t)}^{2}} d x w i t h t ⩾ 0$ $1) s t u d y t h e s e t o f d e f i n i t i o n f o r f (t)$ $2) s t u d y t h e c o n t i n u i t y o f f$ $3) s t u d y t h e d e r i v a b i l i t y o f f$ $4) d e v e l o p p f a t i n t e g r s e r i e$