Evaluate the cross power spectrum, given the cross correlation of two process y (t) and Y (t) is Rxy (6, t + t) = - AB [sin o, t+ cos ag (2t + t)]

Q: 1) (i) Find the gradient of f. (ii) Evaluate the gradient at the point P. f(r, y) = 12y-3 sin(y), P…

A:

Q: When blood flows along a blood vessel, the flux F (the volume of blood per unit time that flows past…

A: Using given information, ∆F=F' ∆R

Q: Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A:

Q: Find the function M(x, y) such that M (x, 0) = eª and the differential equation M(x, y) dx + (sin x…

A:

Q: dx dy = x – y, 2 = x + y ;by using differential operator D find the solution of y. dt Given dt (a) y…

A:

Q: Find dy/dx and d²y/dx2 for r = t2 +t +1 and y = t2 + 2t - 1.

A: given that x=t2+t+1 and y=t2+2t-1 we have to find dydx and d2ydx2 Now,          dydx=dydtdxdt…

Q: Show that the transformation z = log tan (x/2) reduces the differential equation d²y +cotr +4x…

A:

Q: f (x) = 5.6 sin (2.6x – 4.2) – 9.1- What is the equation of the midline of the function %3D o y =…

A:

Q: Cos (x) +ry =4 %3D

A:

Q: Consider g(x, y, z) = ey² + 2y - yArcsinz (a) Find the three (first-order) partial derivatives of g.…

A: Given that , gx,y,z=exyz+2xy-ysin-1z

Q: Consider DE x' (t) = c + x(t)², t≥ 0, ce R. Plot the phase portraits for this DE for all values of…

A: Fixed points of a DE y' = f(t,y) is given by f(t,y) = 0.

Q: 5(c) Calculate the total differential of the following function: 1+ uv 1- u/v g(u, v) =

A: The given problem is to find the total differential of the given function. Given function…

Q: find the integrating factor (x+1)dy - (2y+2x+1)dx = 0

A:

Q: Express the function f(z) = sin(=) in the form f(z) = U (x, y) + V (x, y)i. %3D

A:

Q: z = sin x cos y, = VE, y = 1/t x =

A:

Q: For the function f(x, y) = (cos x)ey +v 1 + x + y. %3D Show the process of using the linearization…

A:

Q: Find the total differential d2 for the dx = 0.01 X= 2 Y = 0 and dy = 0.01 J2 and 42 LE of function…

A:

Q: factor

A:

Q: [ycos + xsin ()]dx = xcos)dy (²)

A:

Q: Estimate the amount of change in f (x, y,z)= cos (7xy)+xz² if the point P(x,y,z) moves a distance of…

A: Given that f(x,y,z) = cos(πxy) + xz2 If the point (x,y,z) moves a distance of ds=0.1units from…

Q: Find the differential dy. (a) y = xv8- x %3D dy %3D (b) y = (1+ x)7 dy

A: