The independent variables X and Y are defined by f(x) = 4ax ; 0 SxSr f (y) 4by; 0 SySs = 0, otherwise = 0, otherwise %3D b-a Show that Cov (U, V) = b + a Where U = x +Y and V =X-Y.

Q: ds if s = Find dt 7t + 3 ds dt II

A: We have given;

Q: 5c) Find the partial derivatives?     y = 2x2+3xz+85w-8z2

A:

Q: Example: Calculate the value of (@w/0x) at the point (x, y, z) = (2, -1,1) if:- w = x2 + y2 + z? z3…

A:

Q: Eliminate the constant: 3x 3x y=c₁₂e³+€₁₂€ ³ Oy"-4y+3y=0 Oy"-6y¹+9y=x Oy"+ 6y' +9y=0 Oy"-6y'+9y=0

A: Given: From the above, we see that the root of the characteristic equation will be 3, 3. So, the…

Q: Find the antiderivative of the functions. S 6x dx S(12x - 5)dx S 3dx S(2x2 + 3)dx 1.) 2.) 3.) 4.)…

A: 1. ∫6x dx2. ∫12x-5dx3. ∫3 dx

Q: Find V. (F x G), if F(x, y, z) = 16xi +j+8yk and G(x, y, z) = xi + yj - zk.

A:

Q: Find fzyr. f(x, y, z) = x³y5₂6 + xy³ + yºz

A: Given: fx,y,z=x3y5z6+xy3+y6z We have to find fzyx For fzyx we first have to find the partial…

Q: ?w Əv у Find when u = 0, v=0 if w=x² + ₁ x=6u-2v + 1₁ y=u+4v - 1.

A:

Q: Find fyx. zyx 5,6 3 f(x, y, z) = x³y2³ + xy + yºz z

A:

Q: iven function

A: In this question, the concept of integration is applied. Integration Integration is a method of…

Q: Determine the function y = eax + b that best fit the data x =(3, 2, 1, 0)T ,y =(µ, 1, e,1/e)T

A: Consider the given information. y=eax+b And, x,y =(3, 2, 1, 0)T ,(µ, 1, e,1e)T=3210,µ1e1e

Q: Let v = (2, (2, 3, 2) 3,

A:

Q: The functions f,6) = ¼cos² #/½ sin %3D are Neither linearly dependent or А. independent B. Linearly…

A:

Q: Find dx (9x² + 16 1 1 - In |3x + V16 + 9x²| + c -In |3x – V16 + 9x²| + c Option 2 Option 3 1 1 In…

A:

Q: = Evaluate S₁2₁,22,23] f (2) dz where 21 = −i, z2 = 2 + 5i, zg 5i and f(x + y) = x² + iy

A:

Q: Eliminate the arbitrary constants y Iny = C,e "+ C, X-

A:

Q: If mZDFC = (11g 9), find g so that FC 1 FD. %3D D F

A: if two line are perpendicular then angle formed is of 90 degree

Q: Consider f(x,y) = xe*y +. Find fx , fy and fxy. y

A:

Q: What does it mean for the differentiability of a function if only one of the Cauchy-Reimann…

A:

Q: Find the partial derivatives of the function က် ထိ စီ ။ ။ ။ w=v4r2 +882 +7t2

A:

Q: if r'y-- 2y + 1.

A:

Q: Find f, (8,2) if f(x.y) = e* - 5y.

A: We can find the answer as below

Q: A) B) dx₁ dt dx₂ dt dx₁ dt dx2 dt dx₁ dt dx₂ Wh = x₁ + 2x₂ + 2x₁.x2 = x₁ + x₂-X1X2 is stable or…

A: Given :           A) dx1dt=x1+2x2+2x1x2    dx2dt=-x1+x2-2x1x2           B) dx1dt=-x1+x2+x12…

Q: |(0,3) C1:x2 + y? = 9. (-3,0) C2 (3,0) Figure 1 Based on Figure 1 and given that F = y²i + (3xy +…

A: We have to find the work done by the vector force F =y2i+(3xy+4x)j Where c is a smooth circle…

Q: Soly

A: Given  u = ( -1 , 0, 1, 1)   v = ( 2, 3, -1, 0)

Q: is selected at random. Find the probability the is female or Republican. What rule will you use?…

A: 5. Consider the table given below:     Political party Total Gender Male 183 144 327 Female…

Q: Determine the vesulting equaton Determine the vesulting equaton after using the suitable…

A: We have to find

Q: 8) y = (x² + 3)ln 4x5 dy (x² + 3) · dx 2x² In 4x° + 5x² + 15 1 - 20x + In 4x³ · 2x 4x A) dy 2х + 1…

A:

Q: The probability histogram to the right represents the number of live births by a mother 47 to 51…

A: Given that A histogram is given here with no. Of child and probability.  By using basic probability…

Q: Let f(x, y) = x³ + y³ + 3x²y + xy + y². Find fæ, fy, fax, fry, fyy.

A: The given function is,