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: f(x, y) = /x² + y?, g(x, y) = x² + y², h(x,y) = 1– a² – y² %3D by inspection, and explain your…

A: using online plotter we can draw the contour plot fx=x2+y2 option b is the correct plot for…

Q: We know that S(x,y)dx + g(x,y)dy] = Se f(x,y)dx +Seg(x,y)dy. Use this knowledge to evaluate S.y dx+x…

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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: 3. Compute the value of F.dr if F = -yi + xj and C is a semicircle from (-1,1) to (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: Find the exact value of F. dr using any method. b. F(x, y, z)= C is the line segment from (1, 0,…

A: The given vector field is Fx, y, z=yz, xz, xy+2z. We have to find ∫CF·dr.

Q: frinal d ouer the disonibed.regian.R. R R「メ=3 fa).

A: We have to use double integration.

Q: f(y) = 3{/v +Vv- 2V a. f'(V) = 12y O b. 9Ny-6Vy-8/y 12y Oc. 9y +6Vy- 8v 12y O d. 9+6Vy +8Vy 12y

A: Topic:- Derivative  correct option = c

Q: Determines the distance between the left right.

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Q: D(3, 7) E(6, 1) F(20, 8) Is the line joining D to E perpendicular to the line joining E to F?

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Q: LL" IIT F4x,y,.2) dz dy dx Sketch and shade representative traces parallel to or in the coordinate…

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Q: %24 1. コト GIPTA Let y be delined implicitly by the following equati function ofXand 2 etz sim (TX2)…

A: The given equation is: exz - sin(πz) -yz =0

Q: Recall the relation between degrees Celsius and degrees Fahrenheit: F = 1.8(C + 32) X and Y are…

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Q: Let X1,..., Xn be i.i.d. Gamma(a, B) with a > 0 and B > 0. Find the MMES of a and В.

A: Let x1, ..., xn be the i.i.d Gamma(α, β) ;α>0, β>0. Find the Method of Moment Estimator of α…

Q: tch the following contour diagrams (cross-sections to the z-axis) to the following fund II) IV) 0.5…

A: Given contour diagrams and their functions. The objective is to match the contour diagrams with…

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: 5. Let (ryz)" a) Compute the directional derivate of f(ay2) at the point (1.1,-1) in the direction…

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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: Calculate Sc(x + y) ds, where C is the rectangle formed by de x=0, x=4, y= -1 and y=1

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Q: Q.IB) If w=f(u, v) where u = tan ¹2 &v=ln(x² + y²), the show that: Əw dw aw +y ax dy 2- ду x-

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Q: l, (2 Y - x ) dA,where R is the region of the first quadrant bounded by the circle x2 + y? = 4 and…

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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: 2 Evaluate the feltowing cartesian integrats by changing them inte equivalent Pelarintegrals: ff dy…

A: As per our guidelines we can solve first question for you .You can ask the remaining questions…

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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