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Math 265 - PowerPoint PPT Presentation


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Math 265. Partial Derivatives. Limits & Continuity. Directional Derivatives. Chain Rule. Approximations. 10. 10. 10. 10. 10. 20. 20. 20. 20. 20. 30. 30. 30. 30. 30. 40. 40. 40. 40. 40. 50. 50. 50. 50. 50. Partial Derivatives – 10 Points. QUESTION: ANSWER :.

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slide2

Partial Derivatives

Limits & Continuity

Directional Derivatives

Chain Rule

Approximations

10

10

10

10

10

20

20

20

20

20

30

30

30

30

30

40

40

40

40

40

50

50

50

50

50

partial derivatives 40 points
Partial Derivatives – 40 Points
  • QUESTION:
  • at (0,-1)
  • ANSWER:
    • 3
directional derivatives 40 points
Directional Derivatives – 40 Points
  • QUESTION:
    • Find the unit vector in the direction in which f increases most rapidly at p:
  • ANSWER:
directional derivatives 50 points
Directional Derivatives – 50 Points
  • QUESTION:
    • Find the plane tangent to
    • at the point (-2,0,-2).
  • ANSWER:
chain rule 10 points
Chain Rule – 10 Points
  • QUESTION:
  • ANSWER:
chain rule 20 points
Chain Rule – 20 Points
  • QUESTION:
  • ANSWER:
chain rule 30 points
Chain Rule – 30 Points
  • QUESTION:
  • ANSWER:
chain rule 40 points
Chain Rule – 40 Points
  • QUESTION:
  • ANSWER:
chain rule 50 points
Chain Rule – 50 Points
  • QUESTION:
    • Find :
  • ANSWER:
approximations 10 points
Approximations – 10 Points
  • QUESTION:
    • Find the equation of the tangent plane at the given point.
  • ANSWER:
approximations 20 points
Approximations – 20 Points
  • QUESTION:
    • Find the equation of the tangent plane at the given point.
  • ANSWER:
approximations 30 points
Approximations – 30 Points
  • QUESTION:
    • Approximate moving from P to Q.
  • ANSWER:
approximations 40 points
Approximations – 40 Points
  • QUESTION:
    • Find all points where the tangent plane is horizontal.
  • ANSWER:
approximations 50 points
Approximations – 50 Points
  • QUESTION:
    • The radius and height of a right circular cone are measured with errors of at most 2% and 3%, respectively. Use differentials to estimate the maximum percentage error in the calculated volume.
  • ANSWER:
    • 7%