The parametric curve Osts is rotated about y-axis. Find the surtace area of the obtained ly= | = sint +t solid.
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- How would I find T(pi/4)? Also how would I find the set of parametric equations for hte line tangent to the space curve at point P?25) Show that the curve with parametric equations x = tcos(t) , y = tsin(t), lz = t ies on the cone z^2 = x^2 + y^2, and use this fact to help sketch the curve.The parametric curve defined by [x = 4t - π · sin(2t) ly = 4 - π· cos(2t) is shown. The curve intersects itself at the point (0,4).
- Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=e^(-3t) cos (8t) y = e^-3t sin (8t) z = e^-3t (1,0,1)Consider the parametric equations x = a cos3 t and y = a sin3 t with 0 ≤ t ≤ π. Find the surface area of the solid obtained by rotating the region about the x-axis.Find parametric equations for line that is tangent to the curve x=cost, y=sint, z=t at the point(cos(4π/6),sin(4π/6),4π/6) Parametrize the line so that it passes through the given point at t=0.
- Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = e−8t cos(8t), y = e−8t sin(8t), z = e−8t; (1, 0, 1)Obtain the differential equation of the family of plane curves described. 1. All ellipses having its centers at the origin and traverse axis x.Find parametric equations for the tangent line at the point(cos(−4π/6),sin(−4π/6),−4π/6) on the curve x=cos(t), y=sin(t), z=(t) x(t)= y(t)= z(t)=