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Limits and Continuity

Limits and Continuity. Definition: Limit of a Function of Two Variables. Let f be a function of two variables defined, except possibly at (x o , y o ), on an open disk centered at (x o , y o ), and let L be a real number. Then:. If for each ε > 0 there corresponds a δ > 0 such that:.

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Limits and Continuity

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  1. Limits and Continuity

  2. Definition: Limit of a Function of Two Variables Let f be a function of two variables defined, except possibly at (xo, yo), on an open disk centered at (xo, yo), and let L be a real number. Then: If for each ε > 0 there corresponds a δ > 0 such that:

  3. 1. Use the definition of the limit of a function of two variables to verify the limit(Similar to p.904 #1-4)

  4. 2. Find the indicated limit by using the given limits(Similar to p.904 #5-8)

  5. 3. Find the limit and discuss the continuity of the function(Similar to p.904 #9-22)

  6. 4. Find the limit and discuss the continuity of the function(Similar to p.904 #9-22)

  7. 5. Find the limit and discuss the continuity of the function(Similar to p.904 #9-22)

  8. 6. Find the limit and discuss the continuity of the function(Similar to p.904 #9-22)

  9. 7. Find the limit (if it exists). If the limit does not exist, explain why(Similar to p.905 #23-36)

  10. 8. Find the limit (if it exists). If the limit does not exist, explain why(Similar to p.905 #23-36)

  11. 9. Find the limit (if it exists). If the limit does not exist, explain why (Hint: think along y = 0)(Similar to p.905 #23-36)

  12. 10. Discuss the continuity of the functions f and g. Explain any differences(Similar to p.906 #43-46)

  13. 11. Use polar coordinates to find the limit [Hint: Let x = r cos(θ) and y = r sin(θ), and note that (x, y) -> (0, 0) implies r -> 0](Similar to p.906 #53-58)

  14. 12. Use polar coordinates and L’Hopital’s Rule to find the limit(Similar to p.906 #59-62)

  15. 13. Discuss the continuity of the function(Similar to p.906 #63-68)

  16. 14. Find each limit(Similar to p.906 #73-78)

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