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Material Type: Exam; Class: CALCULUS III; Subject: Mathematics; University: Temple University; Term: Spring 2007;
Typology: Exams
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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 P 0 (X 0 , Y 0 , Z 0 ) is the point found and
Q is the point Q(1, 1 , 1), then
P 0 Q is 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
− 2
∫ √ 4 −x 2 0
∫ √^4 −x 2 −y 2 0 z
x^2 + y 2 + z 2 dzdydx
− 2
−
√ 4 −x 2
∫ √^4 −x (^2) −y 2 −
4 −x 2 −y 2
z
x^2 + y 2 + z 2 dzdydx
D e
−(x 2 +y 2 +z 2 ) 3 /^2 dV where D is the region that lies below the sphere x (^2) + y 2 + z 2 = 4 and
above z =
x^2 + y 2. 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 =
x^2 + y 2 and above by the sphere x^2 + y 2 + z 2 = 8 and evaluate one of the three integrals.