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Find the point on the surface 6x = y2 + z2 so that its tangent plane is parallel to 3x + 2y - 2z = 1.
3y+ 6z = 11 on the surface 22y2522 = 1 4. Find the closest point to 5. Find the smallest value of r22y2322 if Minimum is at the point , ,9) y + 3z = 4 6. Find the extremes of the following functions over the region R:the triangle (0,0), (1,0) and (1, (a) f(x, y) 3x2+4 Min: 0 at (0,0), Max: 7 at (1,1 (b) f(r, y) = V + Min: 0 at (0,0), Max: 2 at (1,1) (c)...
Find the point on the plane x - 2y ^ 3 * z = 6 that is closest to the point (0, 1, 1) .
Find the point on the plane 3x + 2y + z = 13 closest to the point (1,1,1).
Find the points on the cone z2 =x2 + y2 that are closest tothe point (6, 2,0).
1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone z = x2+y2 Surface Area (1 point) Find the surface area of the part of the plane 2a 4y+z 1 that lies inside the cylinder 2y21. Surface Area2pi
1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone z = x2+y2 Surface Area
(1 point) Find...
1 point Let S be the portion of the sphere z2 + y2 +z2-4above the cone z-cVz2tr where c-1N3 Find the surface area of S Surface Area 2sqrt3 Evaluate the surface integral
1 point Let S be the portion of the sphere z2 + y2 +z2-4above the cone z-cVz2tr where c-1N3 Find the surface area of S Surface Area 2sqrt3 Evaluate the surface integral
1. Find the point on line L that is closest to point P. (a) L: y = 5x - 4, P = (0,9) (b) L: the line through (-1,6) and (3,0), P = (4,5) You need to (i) Draw a graph (ii) Find the equation of L, if not already given (iii) Find the slope perpendicular to L, slope p=- (iv) Find the equation of the line with this two perpendicular slope through P (v) Interesect the two lines
(1 point) Find the point on the line y=6x that is closest to the point P=(1,2) Point = (_ , _)
(a) Find and identify the traces of the quadric surface x2 + y2 ? z2 = 25 given the plane. x = k Find the trace. Identify the trace. y=k Find the trace. Identify the trace. z=k Find the trace Identify the trace. (b) If we change the equation in part (a) to x2 ? y2 + z2 = 25, how is the graph affected? (c) What if we change the equation in part (a) to x2 + y2 +...