Find an equation for the surface obtained by rotating the curve y = √ √x about the x-axis.

The 2D curve 4x2 - y2 = 3, generates a surface in 3D by rotationing it out of the xy-plane and around the x-axis. Create the equation for the surface.

Find the equation of osculating sphere at the origin of the curve x=a₁t³ +3b₁t² +3c₁t₁ y=a₂²³ +3b₂t² +3c₂1, 2=a₂³ +3b₂²2 +3 c₂t

Find the area of the surface generated when the given curve is revolved about the x-axis. y=-x²-2x+8 on [-3, -2] The area of the surface is square units. (Type an exact answer, using as needed.)