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Math 265

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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Math 265

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  1. Math 265

  2. 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

  3. Partial Derivatives – 10 Points • QUESTION: • ANSWER:

  4. Partial Derivatives – 20 Points • QUESTION: • ANSWER:

  5. Partial Derivatives – 30 Points • QUESTION: • ANSWER:

  6. Partial Derivatives – 40 Points • QUESTION: • at (0,-1) • ANSWER: • 3

  7. Partial Derivatives – 50 Points • QUESTION: • ANSWER:

  8. Limits & Continuity – 10 Points • QUESTION: • ANSWER: • -18

  9. Limits & Continuity – 20 Points • QUESTION: • ANSWER: • 3

  10. Limits & Continuity – 30 Points • QUESTION: • ANSWER: • 0

  11. Limits & Continuity – 40 Points • QUESTION: • ANSWER: • DNE

  12. Limits & Continuity – 50 Points • QUESTION: • ANSWER: • 0

  13. Directional Derivatives – 10 Points • QUESTION: • ANSWER: • 1

  14. Directional Derivatives – 20 Points • QUESTION: • ANSWER:

  15. Directional Derivatives – 30 Points • QUESTION: • ANSWER:

  16. Directional Derivatives – 40 Points • QUESTION: • Find the unit vector in the direction in which f increases most rapidly at p: • ANSWER:

  17. Directional Derivatives – 50 Points • QUESTION: • Find the plane tangent to • at the point (-2,0,-2). • ANSWER:

  18. Chain Rule – 10 Points • QUESTION: • ANSWER:

  19. Chain Rule – 20 Points • QUESTION: • ANSWER:

  20. Chain Rule – 30 Points • QUESTION: • ANSWER:

  21. Chain Rule – 40 Points • QUESTION: • ANSWER:

  22. Chain Rule – 50 Points • QUESTION: • Find : • ANSWER:

  23. Approximations – 10 Points • QUESTION: • Find the equation of the tangent plane at the given point. • ANSWER:

  24. Approximations – 20 Points • QUESTION: • Find the equation of the tangent plane at the given point. • ANSWER:

  25. Approximations – 30 Points • QUESTION: • Approximate moving from P to Q. • ANSWER:

  26. Approximations – 40 Points • QUESTION: • Find all points where the tangent plane is horizontal. • ANSWER:

  27. 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%

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