Reference: given by school Course: AP Calculus BC

Calculator Lab S-3 You may use a calculator for any of the following problems, but be sure to show the set-up for your calculations and work. You may not earn full credit otherwise. You MUST round answers to at least three decimal places. 1. The figure below shows the graphs of the line y = 2 and curve C given by x = Vy +7 2 - in the first quadrant. Let R be the region bounded by the two graphs and the .x-axis. The line and the curve intersect at point P. a) Find the coordinates of point P and the value of dy for curve Cat point P. (4 pts.)b) Set up but do not evaluate an integral expression with respect to y that gives the area of region R. (3 pts.) c) Show that curve C is also given by the polar equation r= 7 4cos'0-sine . ( Pts.) d) Use the polar equation in part c to set up an integral expression with respect to the polar angle 0 that represents the area of R. You do not need to evaluate. (4 pts.)2. Consider the curver = 30 + 4sine. a) Write expressions for the x and y coordinates of the curve at the angle 0. Find the coordinates when 0 = -". (3 pts.) b) Find the values of and dy do when 0 = 7. What do these tell us about the curve at that point? (3 pts.) c) Find the value of -or when 0 = . What does it tell us about the curve at that point? (3 pts.) d) Find the value of - do when 0 = T. What does it tell us about the curve at that point? (2 pts.) e) For what value(s) of 0 on the interval ,