Let ?(?, ?) = (? − ?)? + 3? ? + ?^2?. Find an equation of the tangent plane to the surface of ?(?, ?) at the point (−1, 2, 1).

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).
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1 Let f (z, y)5) Find the equation for the tangent plane to the graph of f at the point (3, 3) (Use symbolic notation and fractions where needed.) Hint
1 Let f (z, y)5) Find the equation for the tangent plane to the graph of f at the point (3, 3) (Use symbolic notation and fractions where needed.) Hint
Score: 0 of 1 pt 2 of 10 13.6.11 Find an equation for the plane that is tangent to the given surface at the given point. z = Vy-x (0,1,1) Find the equation for the tangent plane to the surface z = Vy-x at the point (0,1,1). = 0
Partial derivatives
Example Find the equation of the tangent plane and the normal line at the point (1,1,1) to the surface 2x2 + 2y2 + 3z2 = 6. Example Find the equation of the tangent plane and the normal line at the point (1, 2, 3) to the surface 2x2 + y2 – z2 = -3.
1 3. (10 points) Let S be the quadratic surface given by 22-2-y (a) Classify S (B) S is a hyperboloid of one sheet (E) S is an (A) S is an (D) S is an (b) Find the equation of the tangent plane to S at the point (1,1, v3) (C) S is a hyperboloid of two sheets ellipsoid elliptic cone elliptic paraboloid point P(ro.Mo, 20) on S where the tangent plane to S at the point P contains...
Suppose you need to know an equation of the tangent plane to a surface S at the point P(3, 1, 4). You don't have an equation for S but you know that the curves r1()(3 2t, 1 - t2,4 5t+t2) r2(u) (2u2, 2u3 1, 2u 2) both lie on S. Find an equation of the tangent plane at P. Find an equation of the tangent plane to the given surface at the specified point. = 4x2y2-9y, (1, 4, 16) z...
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Find an equation for the plane that is perpendicular to the plane 2.1 + y + 2z = 1 and contains the line Lor=2+t, y = 1+ 4t, z = 1+ 4t. Find the equation of the tangent plane to the surface 2z - 12 = 0 at the point (2,0,2).
5. (2 points) Find the equation of the tangent plane to the given surface ation of the tangent plane to the given surface at point (2. -1,0): sin(xyz) = x + 2y + 3z
Questions 1 and 2
1. Find the gradient of f(I, y) = sin(Zy+5). 2. Let f(x, y, z) - ryz + x) (a) Find the gradient of f. (b) Find an equation of the tangent plane to the level surface ryz + 2 = 5 at the point (2,1,1).
find an equation for the plane tangent to the cone r(r,theta)=(rcostheta)i+(rsintheta)j+rk, r greaterthanorequalto 0, 0 lessthanorequalto theta lessthanorequalto 2pi, at the point P0(-1,sqrt(3),2) corresponding to (r,theta)=(2, 2pi/3). then find a cartesian equation for the surface and sketch the surface and tangent plane together.