Consider the surface f(x.y) = 7-2x - 4y (a paraboloid) and the point P(1,1,1) on the surface. a. Find the gradient of f. b. Let C' be the path of steepest descent on the surface beginning at P, and let C be the projection of C' on the xy-plane. Find an equation of C in the xy-plane. c. Find parametric equations for the path C' on the surface. ....... a. What is the gradient? Vf(x.y) = OD

Q: 3. cos Tx – x*y + e*z + yz = 4 at point Po(0, 1, 2). -

A: The given surface at the point P0 is    Cos(pix) - x2y +exz + yz = 4

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A: The given function is It can be written as as the given function has both variables x and y.

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Q: - Graph the surface 1 = y² + z² — by first sketching at least three cross sections in each of the xy…

A: To Plot: Graph The Surface 1=y2+z2-x24 by plotting at least three cross section in xy and yz plane

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Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y2 + z?…

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A: Formula:

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Q: (b) Find the point that makes the tangent plane to the surface z = x- xy +y-2x + 4y horizontal.

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Q: Find a generating curve on the xz-plane for the surface of revolution with equation x2+ y²+ z²= e2x…

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Q: Find an equation of the plane tangent to the surface z2 - xy = 14 at (2, 1, 4).

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Q: Find an equation of the plane tangent to the surface f(x, y) = xy² – 5x at the poin (1, 2, –1).

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

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