Example Determine the unit tangent vector for r(t) = (t,t³,t5) at the point P = (1,2,3).

Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

Velocity at the Equator Assuming the radius of the earth is 4,000 miles, use the information from Problem 43 to find the linear velocity of a person standing on the equator.