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 mouse Q runs along the positive y-axis at the constant speed v at the origin. A cat P chases the mouse along curve C at the constant speed v starting at point (1, 0) as shown in the following figure. At any time instance, line PQ is tangent to curve C. Determine the equation of curve C.