1. A particle is moving the plane and traces out a curve given by parametric equations :13 = x/gcostrrt) and y = sin(7rt) with 0 g t S 3 seconds. (a) Find the points of the curve where the slope is 1 and write down the equations of tangent lines at those points. (b) Compute the values dE at those points and decide if the graph is concave down or concave up. :1: (G) Let t1 be the smaller of the t values from (a) where the slope is 1. If at that time the object leaves the curve and travels in a line preserving its horizontal and vertical velocities, what is the linear parametric equations for its motion for t 2 t1. 2. Given the curve 2x2y3 + 4my2 313; = 3 answer the following. (a) Verify that (1, l) is on the curve and nd the equation of the tangent line at that point. Also, nd the equation of the normal line at that point. (b) Is the curve concave up or concave down at that point? (c) Estimate a value of b if (0.93, b) is on the curve