Find an equation of the tangent plane to the parametric surface R(u, v) = ((u - sin u) cos v, (1 - cos u) sin v, u) at the point where u = v= FIN
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- Find the equations of the tangent lines to the curve whose parametric equations are r = 2t2 – 4t + ly = 3t – 12t2 + 6; at the point (1, 6).Find an equalion of the tangent plane to the parametric curve given by R(u, v) = ((3 + sin v)sin u, (3 + sin v)cos , u + cos v) at the point where (u,v) = (0,.Find the slope of the tangent line to the parametric curve at (2,e).
- Find 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).Find an equation of the tangent plane to the parametric surface R(u, v) = ((u - sin u) cos v, (1 - cos u) sin v, u) at the point where u = v= TT IN 2Find an equation of the tangent(s) to the curve with parametric equations x = 1+ vt, y = et“ at the point (2, e)
- Find the equation of the tangent line of the parametric equations x = 2 – 3 cos 0, y = 3+ 2 sin 0 at the points (–1,3) and (2,5). .The path r(t)=(5 sin t) i+(5 cos t) j describes motion on the circle x^2+y^2=25. Find the particle's velocity and acceleration vectors at t=π/3 and π/6, and sketch them as vectors on the curve.Consider the parametric equations for a curve in the xy-plane given by: x = t^3 - 3t y = t^2 - 2 Find the equation of the tangent line to the curve at the point where t = 2.
- Find parametric equations for the tangent line at (1, 3, 3) to the curve of intersection of the surface z = x²y and (a) the plane x = 1 (b) the plane y = 3.Let r(t) = cost i + e^t j + t^2 k be given. A) Find the unit tangent vector to the curve at any point. B) Write the parametric equation of the tangent line to the curve at (1,1,0).Find parametric equations for the tangent line at the point (cos(똥), sin(흥), ) cos t, y = sint, z= t on the curve x = 6. x(t) = y(t)= z(t)= (Your line should be parametrized so that it passes through the given point at t=0).