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Lectures 2 and 3 Limits and Continuity of Functions of
Several Variables
Calculus II
Topic 2:
Differential Calculus in Several Variables
Calculus II Santiago de Vicente 1
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Calculus II Santiago de Vicente 2
Please,…remember “Muppets”
…. and Coco (Elmo) Lessons: Learning differences between: • open and closed • disc and ball • interior and exterior • bounded and unbounded • …..
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Intervals, Discs and Balls
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Interior and Boundary Points
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Open and Closed Disks
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“Coco” (“Elmo”) Definitions
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Bounded and Unbounded Sets
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Unbounded Sets
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Unbounded Sets
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Limit of a Function of Several Variables
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Limit of a Function of Several Variables
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Calculating Limits
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Two-Path Test
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Directional Limits (Interior Points)
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Directional Limits (Boundary Points)
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Directional Limits. Examples
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Fundamental Properties
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Some Examples
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Continuity
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Remember one variable Functions
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Remember one variable Functions
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Discontinuity of First Kind
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Some Examples
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Directional Limits (1 of 2)
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Directional Limits (2 of 2)
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More Examples (1 of 2)
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More Examples (2 of 2)
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Composite Functions
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More than two variables
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Homework
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