MATA33H3 Lecture 8: Lecture 8 (10.3 - 10.4)
10.3 Continuity
Most of the functions that you have seen are continuous, or piece - continuous
f(x) = 1 is x is a fraction
-1 otherwise
Definition: (Heuristic)
A function f is continuous on some interval [a, b] if you can draw it’s graph without lifting your pencil
what can go wrong at a so that f is not continuous at a?
To rule out discontinuity at a functions, we require:
f(a) is defined 1.
2.
3.
Definition: A function is continuous t x=a if 1-3 are satisfied
Aside: Set operations. A set is a collection of happy objects, without
Repetition
3
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