Instructor Hentzel Office Phone: 515-294-8141 E-mail: hentzel@iastate.edu Math Department Fax: 515-294-5454 http://www.math.iastate.edu/hentzel/class.166.08 Textbook: Calculus by Varberg, Purcell, Rigdon, ninth edition. Wednesday, April 30 Practice Test 4 The real test is Friday, May 2. 1. Find the area inside r = 3 + Sin[t] 2. Find the area in the first quadrant which is common to both of two curves r = 1 + Sin[t] and r = 1 + Cos[t] 3. Name the curves. (a) r = Cos[t] (b) r = 1 + Cos[t] (c) r = 2 + Cos[t] (d) r = t (e) r t = 1 (f) r = Cos[2 t] 2 (g) r = Cos[2 t] 4. Find the area of one leaf of r = 4 Cos[2 t] 5. Find the slope of r = 3 + 2 Cos[t] at (4, Pi/3) 6. Change this polar equation to rectangular coordinates. 2 r = ----------------- 1 - Cos[t] 7. Find the area of one of the loops of 2 r = 8 Cos[ 2 t] 8. Find the points of intersection of the curves r = 1 + Cos[t] r = 1 - Sin[t] 9. Set up the integral for the length of the Cardioid r = 1+Cos[t] 0 <= t <= 2 Pi. 10. Find all points on the cardioid r = a(1+Cos[t] where (a) the tangent line is horizontal. (b) the tangent line is vertical. 11. (a) Write the rectangular equations for the cycloid generated by a wheel of radius a with parameter t. (b) Find the slope of the cycloid in terms of the parameter t. 12. Let x = 5 Cos[t] and y = 4 Sin[t]. 2 2 Find dy/dx and d y/dx 13. Find the length of the parametric curve defined by 3/2 x = t and y = t 0 <= t <= 3.