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Question Number 36180 Answers: 1 Comments: 1

calculate ∫_0 ^1 ((ln(t))/((1+t)^2 ))dt

$c a l c u l a t e \int_{0}^{1} \frac{l n (t)}{{(1 + t)}^{2}} d t$

Question Number 36179 Answers: 0 Comments: 1

let f(x,y) = ((xy)/(x+y)) 1) find D_f 2)calcule x(∂f/∂x)(x,y) +y (∂f/∂y)(x,y) interms of f(x,y)

$l e t f (x, y) = \frac{x y}{x + y}$ $1) f i n d D_{f}$ $2) c a l c u l e x \frac{\partial f}{\partial x} (x, y) + y \frac{\partial f}{\partial y} (x, y) i n t e r m s o f f (x, y)$

Question Number 36178 Answers: 0 Comments: 1

let f(x,y)=ln((√(x^2 +y^2 ))) calculate (∂^2 f/∂x^2 )(x,y)+(∂^2 f/∂y^2 )

$l e t f (x, y) = l n (\sqrt{x^{2} + y^{2}})$ $c a l c u l a t e \frac{\partial^{2} f}{\partial x^{2}} (x, y) + \frac{\partial^{2} f}{\partial y^{2}}$

Question Number 36177 Answers: 0 Comments: 1

let f(x)= arctan((x/y)) calculate (∂^2 f/∂x^2 )(x,y) , (∂^2 f/∂y^2 )(x,y), (∂^2 f/(∂x∂y))(x,y) (∂^2 f/(∂y∂x))(x,y)

$l e t f (x) = a r c t a n (\frac{x}{y})$ $c a l c u l a t e \frac{\partial^{2} f}{\partial x^{2}} (x, y), \frac{\partial^{2} f}{\partial y^{2}} (x, y), \frac{\partial^{2} f}{\partial x \partial y} (x, y)$ $\frac{\partial^{2} f}{\partial y \partial x} (x, y)$

Question Number 36176 Answers: 0 Comments: 0

let f(x,y) =(x^2 +y^2 )sin{ (1/(√(x^2 +y^2 )))} if(x,y)=(0,0) and f(0,0)=0 prove that f is differenciable at all point of R^2 2) prove that (∂f/∂x) and (∂f/∂y) are not differdnciable at (0,0)

$l e t f (x, y) = (x^{2} + y^{2}) s i n {\frac{1}{\sqrt{x^{2} + y^{2}}}} i f (x, y) = (0, 0)$ $a n d f (0, 0) = 0$ $p r o v e t h a t f i s d i f f e r e n c i a b l e a t a l l p o i n t o f R^{2}$ $2) p r o v e t h a t \frac{\partial f}{\partial x} a n d \frac{\partial f}{\partial y} a r e n o t d i f f e r d n c i a b l e$ $a t (0, 0)$

Question Number 36175 Answers: 0 Comments: 0

let g(x,y) = ((1+x+y)/(x^2 −y^2 )) is g have a limit at (0,0)?

$l e t g (x, y) = \frac{1 + x + y}{x^{2} - y^{2}}$ $i s g h a v e a l i m i t a t (0, 0) ?$

Question Number 36174 Answers: 0 Comments: 0

find lim_((x,y)→(0,0)) ((1−cos((√(xy))))/y)

$f i n d {l i m}_{(x, y) \to (0, 0)} \frac{1 - c o s (\sqrt{x y})}{y}$

Question Number 36173 Answers: 0 Comments: 1

calculate (∂f/∂x) and (∂f/∂y) in this cases 1) f(x,y)= e^(−x) sin(2y +1) 2)f(x,y) =(x^2 +y^2 )e^(−xy) 3)f(x,y) = (x/(x^2 +y^2 ))

$c a l c u l a t e \frac{\partial f}{\partial x} a n d \frac{\partial f}{\partial y} i n t h i s c a s e s$ $1) f (x, y) = e^{- x} s i n (2 y + 1)$ $2) f (x, y) = (x^{2} + y^{2}) e^{- x y}$ $3) f (x, y) = \frac{x}{x^{2} + y^{2}}$

Question Number 36168 Answers: 0 Comments: 3

let A(t) = ∫_(−∞) ^(+∞) ((sin(xt))/(( x +1+i)^2 )) dx with t from R 2) calculate A(t) 2) extract Re(A(t)) and Im(A(t)) 3) find the value of ∫_(−∞) ^(+∞) ((cos(3x))/((x+1+i)^2 ))dx

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

Question Number 36167 Answers: 0 Comments: 2

let give I = ∫_0 ^∞ (dx/((x^2 +i)^2 )) 1) extract Re(I) and Im(I) 2) find the value of I 3) calculate Re(I) and Im(I) .

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

Question Number 36166 Answers: 0 Comments: 1

Find the middle term in the expansion of (x^ + (3/x))^9

$Find the middle term in$ $the expansion of {(x^{} + \frac{3}{x})}^{9}$

Question Number 36163 Answers: 0 Comments: 3

Question Number 36154 Answers: 0 Comments: 0

Q. If x≠y≠z and determinant ((x,x^3 ,(x^4 −1)),(y,y^3 ,(y^4 −1)),((z ),z^3 ,(z^4 −1)))=0 Prove that xyz(xy+yz+zx)=(x+y+z) please help.

$Q . I f x \neq y \neq z a n d | \begin{matrix} x & x^{3} & x^{4} - 1 \\ y & y^{3} & y^{4} - 1 \\ z & z^{3} & z^{4} - 1 \end{matrix} | = 0$ $P r o v e t h a t x y z (x y + y z + z x) = (x + y + z)$ $p l e a s e h e l p .$

Question Number 36153 Answers: 0 Comments: 1

(((x+yi−2)^2 )/(x−yi+1))

$\frac{{(x + y i - 2)}^{2}}{x - y i + 1}$

Question Number 36140 Answers: 1 Comments: 1

Question Number 36148 Answers: 0 Comments: 0

[2^x −^(+ 3) 1 4^(2y+x) x6]=[3^(0−7) 2x]

$[\overset{x}{2} \overset{+ 3}{-} 1 \overset{2 y + x}{4 x 6}] = [\overset{0 - 7}{3} 2 x]$

Question Number 36132 Answers: 0 Comments: 7

a+b=10.........(i) ab+c=0..........(ii) ac+d=6..........(iii) ad=−1...........(iv) (a,b,c,d)=? Note: This problem is related to solve the equation (t^4 +10t+6t−1=0) of Q#35844

$a + b = 10 . . . . . . . . . (i)$ $a b + c = 0 . . . . . . . . . . (ii)$ $a c + d = 6 . . . . . . . . . . (iii)$ $a d = - 1 . . . . . . . . . . . (iv)$ $(a, b, c, d) = ?$ $N o t e : T h i s p r o b l e m i s r e l a t e d t o s o l v e$ $t h e e q u a t i o n (t^{4} + 10 t + 6 t - 1 = 0) o f$ $You can't use 'macro parameter character #' in math mode$