This is a small worksheet that I absolutely need to do well on. Answers are certainly nice but... I also would like to learn the proper way to approach these four problems, if you have time of course!

1. (15 points) Consider the following set of parametric equations: x = 12 + 4t + 3 y = t' + 8t a. Graph the curve represented by these equations. You are encouraged to use your calculator. b. Find each of the derivatives: dx dy dy Show your calculations. dt' dt dx c. Find the equation of the tangent line when t = -2. Explain your answer in terms of the derivatives. d. Find the points of horizontal tangency. e. Find the points of vertical tangency.2. (10 points) Graph the parametric equations and give the integral that calculates the arc length of the curve given by: X = t - 4t +3 my = 6t + 4 t in [0, 2] Approximate the value of this length with your calculator. bos3. (15 points) a. Graph the polar equation r = 3 + 4 sin 0. You may use your calculator, but clearly indicate the points on the graph corresponding to the values 0 =0, 0 = T/6, 0 = Tc/4, 0 = Tt/2, 0 = 5Tt/6, 0 =7Tt/4. b. Find all points of horizontal tangency. c. Find all points of vertical tangency.4. (10 points) Find the area of the common region to the polar curves: r = 5(1 + sin 0) and r = 5(1 - sin 0)