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Question Number 42260 Answers: 0 Comments: 2

let f(a) = ∫_(−∞) ^(+∞) cos(ax^2 )dx with a>0 1) calculate f(a) interms of a ) calculate ∫_(−∞) ^(+∞) cos(2x^2 )dx 3) find the value of ∫_(−∞) ^(+∞) cos(x^2 +x+1)dx .

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

Question Number 42305 Answers: 0 Comments: 6

let f(x) = ∫_(−∞) ^(+∞) ((cos(xt))/((t−i)^2 )) dt 1) let R =Re(f(x)) and I =Im(f(x)) extract R and I 2) calculate R and I 3) conclude the value of f(x) 4) calculate ∫_(−∞) ^(+∞) ((cos(2t))/((t−i)^2 ))dt 5) let u_n = ∫_(−∞) ^(+∞) ((cos((t/n)))/((t−i)^2 ))dt (n natral integer not o) find lim_(n→+∞) u_n and study the convergence of Σu_n

$l e t f (x) = \int_{- \infty}^{+ \infty} \frac{c o s (x t)}{{(t - i)}^{2}} d t$ $1) l e t R = R e (f (x)) a n d I = I m (f (x)) e x t r a c t R a n d I$ $2) c a l c u l a t e R a n d I$ $3) c o n c l u d e t h e v a l u e o f f (x)$ $4) c a l c u l a t e \int_{- \infty}^{+ \infty} \frac{c o s (2 t)}{{(t - i)}^{2}} d t$ $5) l e t u_{n} = \int_{- \infty}^{+ \infty} \frac{c o s (\frac{t}{n})}{{(t - i)}^{2}} d t (n n a t r a l i n t e g e r n o t o)$ $f i n d {l i m}_{n \to + \infty} u_{n} a n d s t u d y t h e c o n v e r g e n c e o f Σ u_{n}$

Question Number 42228 Answers: 1 Comments: 0

Solve : 2x^2 ydx −2y^4 dx+2x^3 dy+3xy^3 dy=0.

$Solve :$ $2 x^{2} y d x - 2 y^{4} d x + 2 x^{3} d y + 3 {x y}^{3} d y = 0 .$

Question Number 42224 Answers: 0 Comments: 5

a + b + c = 180 a,b,c ∈ N number of triplets possible (a,b,c) for the above equation are ? ( the order of a,b,c doesn′t matter)

$a + b + c = 180$ $a, b, c \in N$ $n u m b e r o f t r i p l e t s p o s s i b l e$ $(a, b, c) f o r t h e a b o v e$ $e q u a t i o n a r e ?$ $(t h e o r d e r o f a, b, c {d o e s n}^{'} t$ $m a t t e r)$

Question Number 42222 Answers: 1 Comments: 0

let f(x) =e^(−∣x∣) , 2π periodic even developp f at fourier serie .

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

Question Number 42221 Answers: 1 Comments: 0

Solve: (dt/dx) = (2/(x+t)) .

$Solve :$ $\frac{dt}{d x} = \frac{2}{x + t} .$

Question Number 42215 Answers: 0 Comments: 3

Number of straight lines which satisfy the differential equation (dy/dx) + x((dy/dx))^2 − y =0 is ?

$Number of straight lines which satisfy$ $the differential equation$ $\frac{dy}{d x} + x {(\frac{d y}{d x})}^{2} - y = 0 i s ?$

Question Number 42207 Answers: 1 Comments: 0

Find the equation of tangent and normal to the curve y given by y = x^3 + 3x^2 + 7 .

$F i n d t h e e q u a t i o n o f t a n g e n t a n d n o r m a l t o t h e c u r v e y$ $g i v e n b y y = x^{3} + 3 x^{2} + 7 .$

Question Number 42200 Answers: 1 Comments: 0

Question Number 42199 Answers: 1 Comments: 0

Question Number 42196 Answers: 0 Comments: 4

Let P be an interior point of a triangle ABC and AP,BP,CP meet the sides BC, CA,AB in D,E,F respectively. Show that ((AP)/(PD))= ((AF)/(FB)) + ((AE)/(EC)) .

$Let P be an interior point of a triangle$ $ABC and AP, BP, CP meet the sides BC,$ $CA, AB in D, E, F respectively . Show$ $that \frac{AP}{PD} = \frac{AF}{FB} + \frac{AE}{EC} .$