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Exam 2 Review for Distribution | Calculus III | MATH 2043, Exams of Advanced Calculus

Material Type: Exam; Class: CALCULUS III; Subject: Mathematics; University: Temple University; Term: Spring 2007;

Typology: Exams

Pre 2010

Uploaded on 09/17/2009

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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!4x2
0!4x2y2
0z"x2+y2+z2dzdydx
2. !0
2!0
4x2!4x2y2
4x2y2z"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.

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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 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

  1. Evaluate

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.