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- Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle rolls along the x -axis given that P is at a maximum when x=0.Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces z = x2 + y2 , z = 4 − y at the given point (2, −1, 5).Evaluate √(2² + yz sin(xyz))dx+(y²+xz sin(xyz))dy+(x+xysin(xyz))dz where C is the curve following the outline for the triangle from (1,0,0) to (0,1,0) to (0, 0, 1) and back to (1,0,0).
- Find parametric equations for the line tangent to the curve of intersection of the surfaces tan-1(x? + y? + z²) + e(2 Inx+3In y) – xvz and 15 sec-1(2v2x + 2v2y + v2z) at the point (1, 1, 1).a) Find the equation of tangent line of curve that is given by parametric equations x = 3cost + sint y = e2t at the point (3, 1). b) Find the extrema points of f(x, y) = x³ + 6x² + 3y? – 12xy + 9xFind a set of parametric equations for the tangent line to the curve of intersection of the surfaces x2 + y2 + z2 = 14, x − y − z = 0, at the given point (3, 1, 2).
- Let F(x, y, z) = (6xyz+4x) i+(3a²z+ze-")j+(3x²y-e¬³) k, and let C be the portion of the parametric curve given by x = 6 cos t, y = 6 sin t, z = 3+3 sin(11t/2) that starts at (6,0, 3) and ends at (-6,0,0) (see diagram to the right). Calculate %D F. dr. Show your work, and circle your final answer. (-6, 0, 6), (6, 0, 3) x.Find an equation for the tangent plane to the surface 4xy® + sin(Tx) Z = at the point (1, 1, 4), Find a standard equation for the tangent plane and parametric equations of the normal line at the point P,(2,1, e) on the surface defined by the equation xIn y+ yln z=x.
- Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x2 + y2 and the ellipsoid 3x2 + 2y2 + 6z2 = 29 at the point (−1, 1, 2).Evaluate the line integral (2²yi+ (x- z)j+ zyzk) · dr where C is the parametric curve r(t) = ti + tj + 2k, 0Let C be the curve of intersection of the two surfaces x³ + 2xy + yz = 7 and 3x²-yz = 1. Find parametric equations of the tangent line to C at (1,2,1).SEE MORE QUESTIONS