Consider the curver (t) = (2t, t², In(t)). Starting at the point given by t = 1, I move eº + 2 units along the curve in the positive t direction. What value of t gives the location of the point on the curve I end up at?

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

A gear train consists of three gears meshed together (Figure 9). The middle gear is known as an idler. Show that the angular velocity of the third gear does not depend on the number of teeth of the idler gear (Gear 2).

A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring feet. The ball is started in motion from the equilibrium position with a downward velocity of 8 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) Suppose that aftert seconds the ball is y feet below its rest position. Find y in terms of t. (Note that the positive direction is down.) Take as the gravitational acceleration 32 feet per second per second. y =