In this video, I explore how you can determine the continuity of complicated functions by simply identifying basic functions that make them up and determining from them if they are continuous. I also show why all polynomials and rational functions are continuous everywhere (but in the case of rational functions, wherever they are defined).
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Related Videos:
Continuity: http://youtu.be/_tBGb7Ku-CM
Continuity Examples: http://youtu.be/Wk88MAUFflk
Continuity Part 2 One Sided Continuity: http://youtu.be/1ehfKsXf3wE
Continuity Part 3: Continuity on an Interval: http://youtu.be/f760EuW42dg
Limit Laws - Part 1: Brief Overview: http://youtu.be/qfk5c-43dLg
Direct Substitution for Polynomials - Simple Proof: http://youtu.be/Fnb72ERTLqY
Direct Substitution for Rational Functions - Simple Proof: http://youtu.be/sQa-HqgPonw .
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In the language of algebra, You say that continous functions on given set form a ring (commutative with unity).
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So that's what a ring is in algebra! I had come across "rings" earlier and was wondering to look further into it!
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I don't always deal with complicated functions but when I do I make sure they are continuous ;)
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