Find the highest and lowest point (x, y, z) along the surface 8x +10y+ 4xy – x² – 2yʻ within the region of R (-5, 10), (-5, 0), and (5, 0). Z =

Q: Compute foxy dx + (x³/2+y³/2) dy where C is the square with vertices (0,0), (0,1), (1,1) and (1,0)…

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Q: Use the Lagrange multiplier method to find the point on the surface z = Iy + 10 that is closest to…

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Q: Find the point on the surface x2−2xy+y2−x+y=z closest to the point (1,2,−3) using lagrange…

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

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Q: Find the intersection of the planes x + y + z = 1 and 3x − 2y +z = 5.

A: Consider two planes which are not parallel to each other and intersect. Since planes are three…

Q: Find curl (7z i + 8xj+2y k). curi (7z i+ &x j+ 2y k) = (1 i+( j +( )k

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Q: Calculate (x+y+z) ds

A: In this question, we evaluate the surface integral for the given intersection of the curves.

Q: Find the trace of the plane 3x − 2y + 5z = 4 in the xy-plane.

A: The given equation of the plane is 3x-2y+5z=4. The trace of the plane in the xy-plane is the…

Q: (zy+9)8 dydr

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Q: Use LaGrange multipliers to find the points on the surface 2² = x² + y² which are closest to (4, 2,…

A: Given surface z2=x2+y2 and the point (4,2,0). The objective is to find the points on the surface…

Q: Find the line of intersection between the two planes x+2y-z = 5 and x-4y+z=3

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

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Q: Let F(x,y,z) = 3x²y + 6y³ – 5xz². Find VF ,V²F¸ K×VF, and V×VF.

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

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Q: Integrate f(x,y) = x² + y² over the triangular region with vertices (0,0), (17,0), and (0,17). The…

A: Given: fx,y=x2+y2. We have to integrate the given function over the triangular region with vertices:…

Q: find the points on the surface

A: Given, S: x2-y2+6z=0=fx,y,z where normal line to the surface is parallel to the line passing through…

Q: t G(u, v) = (6u + v, 32u + 9v) be a map from the uv-plane to the xy-plane. Find the image of the…

A: We have to find the equation of line in slope intercept form.

Q: CD has coordinates C(-8,-2) and D(-4,-12). determine the coordiantes of C'D' if (x,y) -> (1/2x,1/2y)…

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Q: $ x4* dx + 2x*y dy where C is the triangle wl vertices (0,0), (3=), and (2, 4) i ?

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