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

Q: Find the area of the surface, which is part of the surface z = 1 + 3x + 2y2 that lies above the…

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Q: Use Lagrange multipliers to find the point on the plane x-y+z=7 closest to the point (4,5,1).

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Q: Find the shortest distance from the origin (0,0) to the hyperbola x² +8xy+7y² = 225. HINT. In the…

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Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 8x – 6y on the circle…

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Q: b) Evaluate the value of I = S(e³y – 3x)dx + (6xey + y)dy, where C' is the parabola - C (0, 0) to…

A: One has to solve it by Green's Theorem.

Q: b) Evaluate the value of I = S(eºy − 3x) dx + (6xey + y)dy, where C' is the parabola y = C (0, 0) to…

A: The integrand is given here as         (e6y - 3x)dx + (6xe6y + y)dy        = (e6ydx + 6xe6ydy) -…

Q: Find the vertex of the paraboloid z=x2+4y2−xy+6x−5y+1

A: The paraboloid is of two type, one is elliptic and another is hyperbolic ,  By suitable choice of…

Q: A laser pointer is situated at the point (3, 1, 4) and is pointing a linear beam in the direction…

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Q: Use Lagrange multipliers to find the point on the plane x − 2y + 3z = 6 that is closest to the point…

A: First note that ,          if (x,y,z) be any point on tha plane x-2y + 3z = 6 then distance between…

Q: What is the center of X x² + y² – 30x + 221 = 0? Show all work for full credit.

A: Topic = Geometry

Q: Draw the standard yz− and xz− traces of the quadratic surface x^2 + y^2 − 2x − z + 1 = 0

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