MATH 201 Final, Fall 2012

Exercise 6 (answer on pages 10, 11 of the booklet) Express the volume V under the parabolic cylinder z = 2? above the region enclosed by the parabola y = 6 — x? and the line y = z in the zy-plane, by using the cartesian coordinates: a) in the order dzdydx b) in the order dzdzdy c) evaluate V Exercise 7 (answer on pages 12, 13 of the booklet) ere {Lee Retry where R is the rectangle bounded by the lines y= a2,y=2+5,y=2-—2, andy=4-—<2 Evaluate Exercise 8 (answer on pages 14, 15, 16 of the booklet) a) Find the work done by (2,3) the force F' = zyi + (y — x)j along the straight line from (1, 1) to American University of Beirut MATH 201 Calculus and Analytic Geometry II] Fall 2012-2013 Final Exam Exercise 1 (answer on page 1, 2 of the booklet) Determine if the following series converges or diverges +00 = b) n+3 ¢) Fae (1- 4)" : er Inn + 2n eal n n=0 n=3 Exercise 2 (answer on pages 3, 4 of the booklet) a) Give the first four terms of the Maclaurin series of f(«) = V2 — @%, then deduce f((0) b) Let f(x,y) be a differentiable function, with 2 = rcos@ and y = rsin@, Use the chain — tule to express f, and fy, in terms of fz, fy, fn)... and 0 Exercise 3 (answer on pages 5, 6 of the booklet) _ Let V be the volume of the eal D in space that is bounded below by the MP ’ by the paraboloid z = x? + y?, and on the sides by the cylinder x? + ORR a a) Express (but do no Exercise 6 (answer on pages 10, 11 of the booklet) Express the volume V under the parabolic cylinder z = 2? above the region enclosed by the parabola y = 6 — x? and the line y = z in the zy-plane, by using the cartesian coordinates: a) in the order dzdydx b) in the order dzdzdy c) evaluate V Exercise 7 (answer on pages 12, 13 of the booklet) ere {Lee Retry where R is the rectangle bounded by the lines y= a2,y=2+5,y=2-—2, andy=4-—<2 Evaluate Exercise 8 (answer on pages 14, 15, 16 of the booklet) a) Find the work done by (2,3) the force F' = zyi + (y — x)j along the straight line from (1, 1) to