MATH 2043 EXAM 2 REVIEW
FOR DISRIBUTION
TEXT: Hass, Weir, Thomas, University Calculus, Pearson Education, Inc., 2007
SECTION 12.4: 5, 10, 12
SECTION 12.5: 6, 11, 18, 21
SECTION 12.6: 3, 6, 7 , 8
SECTION 12.7: 12, 20, 21, 23 ,25, 29, 30
SECTION 12.8: 3, 4, 5, 10, 11, 17 (Also in problem 17 show that if P0(X0,Y
0,Z
0) is the point found and
Qis the point Q(1,1,1), then −−→
P0Qis normal to the plane x+2y+3z= 13
SECTION 13.1: 7, 9, 10, 15, 19, 20
SECTION 13.2: 5, 6, 21, 25, 27, 28, 31
SECTION 13.3: 3, 5, 7, 8
SECTION 13.4: 9, 10 11, 13, 15, 37 , 39
SECTION 13.5: 5 (evaluate one way), 9, 11, 17, 27, 28 , 30, 32
SECTION 13.7: 4, 5, 8, 11 (a& b), 31, 37, 53
Convert to cylindrical coordiates and evaluate
1. !2
−2!√4−x2
0!√4−x2−y2
0z"x2+y2+z2dzdydx
2. !0
−2!0
−√4−x2!√4−x2−y2
−√4−x2−y2z"x2+y2+z2dzdydx
3. Evaluate ! ! !De−(x2+y2+z2)3/2dV where Dis the region that lies below the sphere x2+y2+z2= 4 and
above z="x2+y2.
Review Exercises Chapter 13 — 17, 18, 19, 20, 31
Also, Set up integrals in rectangular, cylindrical and spherical coordinates to find the volume of the region
bounded below by the cone z="x2+y2and above by the sphere x2+y2+z2= 8 and evaluate one of
the three integrals.