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) co...
The tangent plane at a point Po(f(uo.VO) 9 (uo.vo) h(uo,VO)) on a parametrized surface r(u,v) = f(u,v) i + g(u,v) j+h(u, v) k is the plane through P, normal to the vector ru (uo.VO) XIV(40.VO) the cross product of the tangent vectors ru (uo. Vo) and rv (uo.VO) at Pg. Find an equation for the plane tangent to the surface at Po. Then find a Cartesian equation for the surface and sketch the surface and tangent plane together. (573 15...
For the polar equation r= 1-sinθ a) Sketch the graph for 0 ≤ t ≤ 2pi b) Find the points on the cardioid where the tangent line is horizontal c)Find the equation of the tangent line when theta=pi/3
Find the equation of the line tangent to the r(t)=(t^2+t)*i+sqrt(t)*j when t=3
Find an equation of the tangent plane to the cone 4z2 = x2 - 9y2 at the point (5, −1, 2)
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)...
Find the equation for (a) the tangent plane and (b) the normal line at the point P (9,0,9) on the surface 8z - -0. (a) The equation for the tangent plane is I.
For the elliptic-paraboloid find the Cartesian equation of the tangent plane at the point on the surface where x = -2 and y = 1. Your answer should be an equation, expressed in terms of the Cartesian variables x, y and z using the correct syntax. For example: 3*x-2*y+5*z=2, or, 2*(x-1)+4*(y-2)+z-1=0, or 3*x+ 6*z=12-y, or y-x+35*(z-256)=20 Do not use decimal approximations all numbers should be entered as exact expressions, for example 5/2 2x2+y2-10-2, 0 < z < 10 2x2+y2-10-2, 0
Given f(x, y): 10-2x2-y, find a) The equation of the tangent plane to the surface at the point (2.2,6) b) The parametric equations of the normal line at the point (2, 2, 6) c) The outward unit normal vector to the surface at the point (2, 2,6) d) Sketch the surface and the outward unit normal vector at the point (2, 2,6). 1. Given f(x, y): 10-2x2-y, find a) The equation of the tangent plane to the surface at the...
1. Find the volume of the solid under the cone z= sqrt (x^2 + y^2) and over the ring 4 |\eq x^2 + y^2 |\eq 25. 2. Find the volume of the solid under the plane 6x + 4y + z= 12 and over the disk with border x^2 + y^2 = y. 3. The area of the smallest region, locked by the spiral r\Theta= 1, the circles r=1 and r=3 and the polar axis.
Find an equation of the tangent plane to the following parametric surface, r(u, v) = (u2 + 9) i + (v3 + 6u) j + (u + 2v) k , at the point (10, 5, −1). Write the equation in the form ax + by + cz + d = 0, where a, b, c, and d have no common factors. Then enter the values of a, b, c, and d (in that order) into the answer box below, separated...