4) Let h(x, y) = 2x² + y² – 2x²y. Find the absolute minimum and maximum values of the surface on the rectangular region -2 ≤ x ≤ 2 and 0 ≤ y ≤ 3.

Q: Find the minimum distance from the point (2, -1, 1) to the plane x + y - z = 2.

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Q: Find the maximum volume of a rectangular box with faces parallel to the coordinate planes if one…

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Q: Find the maximum and the minimum values of f(x,y,z) = 5x -8y + 8z on the sphere x² + y² + z² = -

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Q: 5) Find the maximum and minimum values that 3x - y - 3z attains on the intersection of the surfaces…

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Q: 3. Find the area of the part of the surface x 2z + y° - 3, that lies above the triangle in the…

A: Given, x=2z+y2-3, i.e. z=12x-y2+3. As it is known that the surface area is given as,…

Q: 1/ Find maximum,minimum Z= x³y³-12x + 3y + 12. ,and saddle point of the surface

A: Use the method of Lagrange multipliers to find maxima minima of the given function as in next step.

Q: Identify and sketch the quadric -- = 0 3 2 3 surface z 2

A: For the solution of the problem follow the next step.

Q: Describe and draw at least 3 level surfaces for the function f(r, y, z) = x²+ y? - z?

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Q: Describe and sketch the following surfaces z = f(x, y): (a) * (c) 2= /1-x² - y² z = 6 - 2x - 3y (b)…

A: We have to sketch and describe the following curve

Q: Sketch the surface x = 2y2 +3z2

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Q: What kind of surfaces are the level surfaces f(x, y, z) = const? f = 4x - 3y + 2z

A: As per the question we are given a trivatiate function : f(x, y, z) = 4x - 3y + 2z And we have to…

Q: Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the…

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Q: Sketch a typical level surface for the function f(x,y,z) = 3x² + 3y² + 3z².

A: Given that the function is                       f(x, y, z)=3x2+3y2+3z2.