3(x + y) cos (x2 - y?) da, where R is the rectangle enclosed by the lines x - y = 0, x – y = 6, x + y = 0, and x + y = 6 Hints: If we set u = x-y, v=x+y, how are x and y expressed in terms of u and v; which region D in the uv-plane is mapped to R in the xy-plane; what is the Jacobian of x,y with y.v?

Q: d: x = -2. d2: y+1_z-1 -1 -2 x+3_y-2 -2_Z-4 2 1 -1

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Q: 4. By using Cramer's rule, find the value óf Y: 2x +3y-2=16 5X-y +2Z = 36 X + 2y -42 =5

A: We have given that  2x+3y-z=16 5x-y+2z=36 x+2y-4z=5       In matrix form  23-15-1   212-4xyz=16365…

Q: Determines the distance between the left right.

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Q: Which of the following functions maps the red function (y=x)onto the image function? a) y = -x+2|…

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Q: 2) The contour map of f(x, y) is shown below. Use it to find fx (1,3) 10 10 8 8 6 =2 6 0 x=2 6 8 10

A: fx​(1,3)=1   Explanation:From the given contour map, we can see that, f(1,3)=4  Similarly we can…

Q: a. In R?, let C be the line segment from (-1,2) to (0, 4), and let F = (x + 2,-xy). Evaluate S, F ·…

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Q: Evaluate y ds, C: x = t², y=t, -5 < t < 4 C

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Q: If the given three vectors are coplanar, then find the value of x. A = i-2j + 3k, B = xj + 3k, C =…

A: A, B, C are coplanar.So

Q: (a) Referring to the below picture, suppose that F(r, y) = (P(r,y), Q(r, y)), Sc, F-ds = 3m and Sc…

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Q: Let T : R^2 → R^3 be a linear map. What are the possibilities for the pair of numbers (dim Null…

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