2. Consider the surface S with parametrization r(s, t)< st, s,t3 - s >. Find parametric equations...
(1 point) Consider the surface with parametric equations r(s, t) = (st, s +t, s – t). A) Find the equation of the tangent plane at (2,3,1). B) Find the surface area under the restriction sa + t2 <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...
Consider the surface given by the parametric equations . Let P be the point (4,0,6). Find an equation of the tangent plane to the surface at the point P. r=< u2, 2ucos(v), 3usin() >
(1 point) A parametric curve r(t) crosses itself if there exist t s such that r(t)-r(s). The angle of intersection is the (acute) angle between the tangent vectors r() and r'(s). The parametric curver (2 -2t 3,3 cos(at), t3 - 121) crosses itself at one and only one point. The point is (r, y, z)-5 3 16 Let 0 be the acute angle between the two tangent lines to the curve at the crossing point. Then cos(0.997 (1 point) A...
A surface S described as circular paraboloid x2 + y2-z bounded by plane z-3. a) Find a parametrization for S. b) Find plane tangent to S at (1, 1, 2) A surface S described as circular paraboloid x2 + y2-z bounded by plane z-3. a) Find a parametrization for S. b) Find plane tangent to S at (1, 1, 2)
Find an equation for the tangent plane and parametric equations for the normal line to the surface at the point P. x2 – xyz = 228; P(-6,8,4) Equation for the tangent plane: Edit Parametric equations for the normal line to the surface at the point P: Edit Edit z = 4 + 481
Question 8 Find an equation for the tangent plane and parametric equations for the normal line to the surface at the point P. sin 20 Tangent Plane: z= ? Edit Normal Line: x(t) = ? Edit ) = Edit z(t) = 1 - 1 MapleNet
Question 8 Find an equation for the tangent plane and parametric equations for the normal line to the surface at the point P. Р 14 Tangent Plane: z= Edit Normal Line: X(t) = ? Edit y(t) = Edit z(t) = 1-t
Find an equation of the tangent plane and parametric equations of the normal line to the surface ?? − ?? 3 + ?? 2 = 2 at the point ?(−1, −1, 2).
please answer both (12(8 pts) Find parametric equations of the line through the point (2, -1,3) and perpendicular to the line with parametric equations 1-t,y 4- 2t and 3+ t and perpendicular to the line with parametric equations 3+t,y 2-t and z 3+2t. (13)(8 pts) Find the unit tangent vector (T(t) for the vector function r(t) - costi+3t j+ 2sin 2t k at the point where t 0 (12(8 pts) Find parametric equations of the line through the point (2,...