Find the image of the Gauss map of the FINITE portion of the paraboloid z = x^(2) + y^(2) , z smaller than or equal to 1 with respect to the outward unit normal

A point moves along the curve of intersection of the paraboloid z=x^2+5y^2 and the plane x=3. At what rate is z changing with y when the point is at (3,-1,14)?

Find the equation of the plane tangent to the surface of Z = x^2 + y^2 at point P(1, 2, 5).

Consider the curve C consisting the the portion of the parabola y = x2 from (2, 4) to (-2, 4) together with the line segment from (-2, 4) to (2, 4). (a) Is C positively or negatively oriented? O Positively oriented O Negatively oriented (b) Let F(x,y) = (e2xy+cos(7x²), xºy^+e5y) Use Green's Theorem to set up the line integral F. dr as an iterated double integral in the dydx order. ) dy dx

Find an equation of the tangent plane to the surface x2 + y2 + z2 = 9 at the given point (1, 2, 2) and find a set of symmetric equations for the normal line to the surface at the given point.

Draw a contour map for f(x,y) = x^2 + 4y^2 where k = 3, k=8 and k=14

Above xy plane

Find the vector equation that represents the curve of intersection of the paraboloid z=3x^2+y^2 and the surface y=x^3. Write the equation so that one of the functions is simply t.

Find a vector function that represents the curve of intersection of the surface 4x+2y-8z^2=16 and the cylinder of radius 3 wrapped around the y-axis.