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12.1 Introduction to Functions of Several Variables

• EXC 45
• EXC 46
• EXC 47
• EXC 48
• 12.2
• 12.3
• 12.11
• 12.14
• 12.16
• 12.17
• Table top a
• Table middle a
• Table middle b
• Table bottom a
• Table bottom b
• Table bottom c

12.10 Lagrange Multipliers

• 12.80
• 12.79
• EXC 26
• EXC 32

12.2 Limits and Continuity

• 12.22
• 12.21
• 12.24
• 12.25
• 12.27
• 12.26
• EXC 17
• EXC 18
• EXC 19
• EXC 20
• EXC 21
• EXC 22
• EXC 23

12.3 Partial Derivatives

• EXC 33
• EXC 34
• EXC 35
• EXC 36
• 12.29
• 12.30
• 12.31b
• 12.31a

12.4 Differentials

• Technology
• 12.38
• 12.35

12.6 Directional Derivatives and Gradients

• 12.47
• 12.49
• 12.53
• 12.42
• 12.44
• EXC 51
• EXC 52

12.7 Tangent Planes and Normal Lines

• EXC 15
• EXC 17
• EXC 16
• EXC 18
• Technology a
• Technology b
• 12.57
• 12.58
• 12.59
• 12.62
• 12.60

12.8 Extrema of Functions of Two Variables

• EXC 25
• EXC 26
• EXC 27
• EXC 28
• 12.64
• 12.68
• 12.69
• 12.70
• 12.71
• 12.63
• 12.67

12.9 Applications of Extrema of Functions of Two Variables

• 12.72

Chapter Opener

• Chap Opener 12

12 Review Exercises

• REV EXC 1
• REV EXC 2