In this problem we use the change of variables x = 3s + t, y = s t to compute the integral √(x + y) dA, where R is the parallelogram with vertices (x, y) = (0, 0), (6, 2), (8, 0), and (2,-2). First find the magnitude of the Jacobian, Then, with a = C = √(x + y) dA= fb fd ( , and d = d(x,y) d(s,t) ,b= S+ = t+ ) dt ds =

Q: 7. State the linearization, L(r, y), of f(x, y) for the point (4, 3). f(x, y) = x3/² y Next, use the…

A: Given that  f(x,y)=x^(3/2)y  To find the linearization of f(x,y)

Q: F(x, y,z)= (4xyz) î + (-2xz+2yz) ĵ -3y² z k , find VxF

A:

Q: Find the orthogonal trajectories of the family of lines 3x + 5y = C A B C D 3x 5y = k 5x 3y = k 3x +…

A: Orthogonal trajectory

Q: Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].

A:

Q: Let C = (-2, -1) be the center of dilation. Let X = (1, 1), Y = (3, 0) and Z = (2,5). Our dilation…

A: Center of dilation=-2, -1X=1, 1, Y=3, 0, Z=2, 5Dilation factor, k=3

Q: (c) If f is a C² scalar function, then V × (Vƒ) = 0. True False (d) The lines 1₁ (t) = (1 − t, 1+ t,…

A: (C) If c is scalar function Means      curl(grad ƒ)  is = 0   Therefore correct ans is  True

Q: (3,8, 0) is u x v = %3D So the cross product of u = (1, 0, 1) and v =

A:

Q: Suppose F(x, y) = (x² + 6y, 2x − 2y²). Use Green's Theorem to calculate the circulation of around…

A:

Q: Evaluate I= √ (sinx+2y) dx + (6x+y)dy for the non closed path ABCD in the figure.

A:

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

A:

Q: Two sharpshooters will simultaneously shoot once at a target. Let Xi , i = 1, 2, be marksman i's…

A: Given that, the errors are modelled by X1~N(0,0.5),X2~N(0,1). To solve this problem z table values…

Q: Compute the Jacobian for the substitutions x = ρsinφcosϴ,  y = ρsinφsinϴ,  z = ρcosϴ.

A:

Q: Compute F. dr where F (x,y) (6x + y) i+ (4y + x)j and C is a piecewise curve from the point (1,1) to…

A: