MAT 21A Lecture 5: MAT21A - Lecture 5 - 2.5: Continuous Functions Part 1
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Mat21a - lecture 5 - 2. 5: continuous functions part 1. Intuitively, a continuous function is one which can be graphed without lifting your pencil (high school definition) These are the only reasons why a function might not be continuous: Let"s look at these graphs: y = f (x) y = g (x) Not continuous at 3 because f(x) is not defined at 3. Not continuous at 4 because does not exist (x) lim x 4 g. Not continuous at 5 because (x) = (5) / h h lim x 5 y = h (x) F(x) is continuous at x = c means: (c) f lim x c lim x c exists f (x) (x) f. X is continuous at 5 would not be continuous at -2 because -2 is not in the domain is not a real number) Reasons why f(x) might not be continuous at x = c:
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