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Chapter 7

Chapter 7. Functions of Several Variables. Figure 7.1: Three-Dimensional Coordinate System. Figure 7.4: Distance and Midpoint Formulas. Distance Formula in Space. Midpoint Formula in Space. Figure 7.6: Standard Equation of a Sphere. Figure 7.10: General Equation of a Plane.

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Chapter 7

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  1. Chapter 7 Functions of Several Variables

  2. Figure 7.1: Three-Dimensional Coordinate System

  3. Figure 7.4: Distance andMidpoint Formulas

  4. Distance Formula in Space

  5. Midpoint Formula in Space

  6. Figure 7.6: Standard Equationof a Sphere

  7. Figure 7.10: General Equationof a Plane

  8. Figure 7.12: Planes Parallelto Coordinate Planes

  9. Figure 7.13: Planes Parallelto Coordinate Axes

  10. Figure 7.14

  11. Elliptic Cone

  12. Elliptic Paraboloid

  13. Hyperbolic Paraboloid

  14. Ellipsoid

  15. Hyperboloid of One Sheet

  16. Hyperboloid of Two Sheets

  17. Definition of aFunction of Two Variables

  18. Figure 7.19: Contour Mapsand Level Curves

  19. Partial Derivatives of aFunction of Two Variables

  20. Notation for First Partial Derivatives

  21. Figure 7.23: Graphical Interpretationof Partial Derivatives

  22. Figure 7.26: Relative Extremaof a Function of Two Variables

  23. Figure 7.28: First-PartialsTest for Relative Extrema

  24. Second-Partials Testfor Relative Extrema

  25. Figure 7.34: Finding aMaximum Value

  26. Method of Lagrange Multipliers

  27. Figure 7.37: Measuring theAccuracy of a Mathematical Model

  28. Figure 7.38: Sum of theSquared Errors

  29. Definition of the Sumof the Squared Errors

  30. The Least SquaresRegression Line

  31. Least SquaresRegression Quadratic

  32. Determining Area in thePlane by Double Integrals

  33. Figure 7.48: Volume ofa Solid Region

  34. Determining Volumeby Double Integrals

  35. Guidelines for Findingthe Volume of a Solid

  36. Average Value of aFunction over a Region

  37. Algebra Summary:Solving Systems of Equations

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