# MATA31H3 Lecture 5: week 5

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## Document Summary

5. 1 continuity at a point and on an interval. Intuitively we thought of continuous functions as of functions with graphs we can sketch. Without picking up our pencil in this section we"ll develop a formal definition of continuity using limits. , we say that f is continuous at c if (c p, c + p) f (x) = f (c) lim x c. Graph of continuous function f is continuous at every number in an interval (has no breaks in this interval) The above implies: is defined (c is in the domain of f(x)) f (c) lim x c lim x c f (x) exists f (x) = f (c) f (x) Types of discontinuities is discontinuous at c if one of the (1), (2), or (3) fails. If function f defined on open interval (c p, c + p) , we say that f is continuous at c if for each.