2) Instructor's Questions Consider the surface given by 2-222 + y2 = 1. (a) Show that...
7. Let S be surface, oriented upward, given by the graph of f(x, y) 2 - z2 -y2 which lies over the unit disk in the ry-plane. If F(, y,z (-4x+ 1 + 3y2 1 +3y2 7. Let S be surface, oriented upward, given by the graph of f(x, y) 2 - z2 -y2 which lies over the unit disk in the ry-plane. If F(, y,z (-4x+ 1 + 3y2 1 +3y2
5 and 6 please 5) Given the surface f(x, y, z) = 0 or z = f(x,y), find the tangent plane at P. a) z2 – 2x2 – 2y2 = 12 @ P=(1,-1,4) b) f(x,y) = 2x - 3xy3 @ 12,-1) c) f(x,y) = sin(x) @ (3,5) 6) Find an equation of the tangent plane and the equation of the normal line to surface f(x..zb=0 @P x2 + y2 + z2 = 9 P = (2,2,1)
7) Consider the surface S: x2 +y2 - z2 = 25 a) Find the equations of the tangent plane and the normal line to s at the point P(5,5,5) Write the plane equation of the plane in the form ax + By + y2 + 8 = 0 and give both the parametric equation and the symmetric equation of the normal line. b) Is there another point on the surface S where the tangent plane is parallel to the tangent...
Cal 4 , ) and use this to 6. Let f(x,y) = x2 + y2 + 2x + y. (a) Find all critical points of f in the disk {(x,y) : x2 + y2 < 4). Use the second derivative test to determine if these points correspond to a local maximum, local minimum, or saddle point. (b) Use Lagrange multipliers to find the absolute maximum/minimum values of f(x, y) on the circle a2 +y -4, as well as the points...
do 9 e it with the actual change. k, find vectors u, o, such that the three dicular local critical points of the function f(z, y) = x2 +y2-2x + 1; 1y Is a local minimum, local maximum, or saddle point. em 8. Where is the tangent plane horizontal for the surface Find the largest possible volume of the rectangular box in the first t with Problem 9 three faces in the coordinate planes and one vertex in the plane...
1. Consider the surface of revolution that is given by the equation Z-R= -(x2 + y2)/R where [x],[y] < R/V2 . (a) Find the volume enclosed between the surface and the x-y plane. (b) Find the normal vector în and an equation for the tangent plane to the surface at i = ? (î+ ſ + Â). (Hint: Choose appropriate coordinate systems in each part).
Please explain b! 2. Let z = f(x, y) = ln(4x2 + y2) (a) Use a linear approximation of the function z = f(x,y) at (0,1) to estimate f(0.1, 1.2) (b) Find a point P(a,b,c) on the graph of z = f(x, y) such that the tangent plane to the graph of z = f(x,y) at the point P is parallel to the plane 2x + 2y – 2=3
Find an equation of the plane tangent to the following surface at the given point. yz e XZ - 21 = 0; (0,7,3) An equation of the tangent plane at (0,7,3) is = 0. Find the critical points of the following function. Use the Second Derivative Test to determine if possible whether each critical point corresponds to a local maximum local minimum, or saddle point. If the Second Derivative Test is inconclusive, determine the behavior of the function at the...
Check that the point (1,-1,2) lies on the given surface. Then, viewing the surface as a level surface for a function f(x,y,z), find a vector normal to the surface and an equation for the tangent plane to the surface at (1,-1,2). 2x^2-3y^2+z^2=3. Vector normal? and tangent plane?
true or false is zero. F 9. The plane tangent to the surface za the point (0,0, 3) is given by the equation 2x - 12y -z+3-0. 10. If f is a differentiable function and zf(x -y), then z +. T 11. If a unit vector u makes the angle of π/4 with the gradient ▽f(P), the directional derivative Duf(P) is equal to |Vf(P)I/2. F 12. There is a point on the hyperboloid 2 -y is parallel to the plane...