5. (2 points) Find the equation of the tangent plane to the given surface ation of...
Find the equation of the plane tangent to the following surface at the given points. x2 + y2 - 2? + 5 = 0; (4,2,5) and (-2,-4,5) The equation of the tangent plane at (4,2,5) is = 0. the equation of the tangent plane to the surface
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...
Which of the following is the equation of the plane that is tangent to the surface 222 + y² - zz-32= -1 at the point P (1,-1,1)? 3 x + 2y - 42 = -3 5x – 2y - 42 = 3 3x - 2y - 32 = 2 3x - 2y - 42 = 1 52 – 2 – 3z = 4 00 Mark This Question
1) Assume you are given the surface S with equation 2 1- (a) Find the equation of the tangent plane to S at the point (V6, 1) (b) Find a point on the surface S so that the tangent plane to S at that point contains the point (3,0, 0). (c) Give an equation for and geometrically describe the set of points on S so that the tangent plane to S at those points contains the point (3, 0,0). 1)...
Exercise 1. Tangent plane (15 pts) Let (5) be the surface given by the following equation. x2+y2 = 1+z2 An equation of the tangent plane to (S) at A(1,2,2) is: a. 2x + 4y – 4z = 1 b. x + y - z=0 c. x + 2y – 2z = 1 d. x + y - z = 2 e. None of the above a. b. C. O d. e. Exercise 2. Directional derivative (6 pts + 9 pts)...
Find an equation of the plane tangent to the following surface at the given points. z = 4 cos (x - y) + 2; л л 3 3 ,0 and 6.6
7. Find an equation of the tangent plane to the given parametric surface r(u, v) = uvi+u sin(n)j + v cos(u)k, at u = 0, v = . 8. Find the area of the part of the surface 2 = 2 + 5x + 2y that lies above the triangle with vertices (0.0), (0,1), and (2,1).
3.(10 points) Find an equation of the tangent plane to the surface (a) z = xe” at the point P(1,0,1). (6) sin xz - 4 cos yz = 4 at the point P(11,1,1).
Find an equation of the tangent plane to the given surface at the specified point. z = y In(x), (1, 8, 0)
Find an equation of the tangent plane to the given parametric surface at the specified point.r(u, v) = u cos vi + u sin vj + vk; u = 9, v = p/3