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(1 point) Consider the surface with parametric equations r(s, t) = (st, s +t, s –...
2. Consider the surface S with parametrization r(s, t)< st, s,t3 - s >. Find parametric equations and symmetric equations for the tangent plane to S at the point (1, 1,0). 2. Consider the surface S with parametrization r(s, t). Find parametric equations and symmetric equations for the tangent plane to S at the point (1, 1,0).
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() >
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...
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
1. a. Consider the curve defined by the following parametric equations: r(t) = et-e-t, y(t) = et + e-t where t can be any number. Determine where the particle describing the curve is when tIn(3) In(2). 0, ln(2) and In(3). Split up the work among your group Onex, vou l'ave found i lose live polnia, try to n"惱; wbai ille wlu le curve "u"ht lex k like. b. Verify that every point on the curve from the previous problem solves...
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
2. Consider the parametric equation of a cycloid, given by r=r(@- sin()), y = r(1 - cos(@)). (1) Find the equation of the tangent line to the cycloid at the point where @ = 7/4. (2) Find the area under one arch of the cycloid (0 SO2 ). (3) Find the length of one arch of the cycloid.
(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...
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).