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Chapter 14 – Partial Derivatives

Chapter 14 – Partial Derivatives. 14.2 Limits and Continuity. Objectives: Determine the limit of functions of two variable Determine if a function of two variables is continuous. Definition – Limit of f ( x , y ). Other limit notation:.

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Chapter 14 – Partial Derivatives

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  1. Chapter 14 – Partial Derivatives 14.2 Limits and Continuity • Objectives: • Determine the limit of functions of two variable • Determine if a function of two variables is continuous 14.2 Limits and Continuity

  2. Definition – Limit of f(x, y) 14.2 Limits and Continuity

  3. Other limit notation: • There are other ways to write the limit of a function. 14.2 Limits and Continuity

  4. Example 1 • Find the limit, if it exists, or show that the limit does not exist. 14.2 Limits and Continuity

  5. Visualization • Limit Does Not Exist 14.2 Limits and Continuity

  6. Example 2 – pg. 899 # 14 • Find the limit, if it exists, or show that the limit does not exist. 14.2 Limits and Continuity

  7. Example 3 – pg. 899 #16 • Find the limit, if it exists, or show that the limit does not exist. 14.2 Limits and Continuity

  8. Definition - Continuous 14.2 Limits and Continuity

  9. Intuitive Meaning • The surface that is continuous has no holes or breaks. 14.2 Limits and Continuity

  10. Example 4 • Determine the set of points at which the function is continuous. 14.2 Limits and Continuity

  11. Example 5 – pg. 900 #34 • Determine the set of points at which the function is continuous. 14.2 Limits and Continuity

  12. Example 6 – pg. 900 # 37 • Determine the set of points at which the function is continuous. 14.2 Limits and Continuity

  13. More Examples The video examples below are from section 14.2 in your textbook. Please watch them on your own time for extra instruction. Each video is about 2 minutes in length. • Example 1 • Example 3 • Example 5 14.2 Limits and Continuity

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