MTH 201 Final, Fall 2012

Final Exam Exercise 1 (answer on page 1, 2 of the booklet) Determine if the following series converges or diverges = n+3 2" i\" ‘ oF att 9 Fe(-2) vive sag N+ Qn ope n Exercise 2 (answer on pages 3, 4 of the booklet) a) Give the first four terms of the Maclaurin series of f(a) = 2 — 2%, then deduce f*)(0) b) Let f(a,y) be a differentiable function, with « = rcos@ and y = rsain@, Use the chats tule to express f, and fy, in terms of fz, fy, fra)... and 0 Exercise 3 (answer on pages 5, 6 of the booklet) Let V be the volume of the gal D in space that is bounded below by the ak. by the ihe z=? +y?, and on the sides by the cylinder x? +(y~ 1)? = ot i: a) ‘Saee (out. de not e Exercise 6 (answer on pages 10, 11 of the booklet) Express the volume V under the parabolic cylinder z = x? above the region enclosed by the parabola y = 6 — x? and the line y = z in the ry-plane, by using the cartesian coordinates: a) in the order dzdydx b) in the order dzdrdy c) evaluate V Exercise 7 (answer on pages 12, 13 of the booklet) Evaluate Rf where RF is the rectangle bounded by the lines y= 7,y=2+5,y=2-—2, andy=4-—2 Exercise 8 (answer on pages 14, 15, 16 of the booklet)