MATH116 Lecture 16: lect116_10_f15

• School: University of Waterloo
• Department: Mathematics
• Course: MATH116
• Professor: Fiona Dunbar

Document Summary

Friday, october 2 lecture 10 : continuous functions. (refers to section 2. 4 in your text) Students who have mastered the content of this lecture know about: The definition of f is continuous at a , continuity from the left or right of a, a function being continuous on an interval, the basic properties of continuous functions. 10. 1 definition a function f (x) is continuous at a point a if limx a f (x) = f (a). 10. 1. 2 proposition the function f (x) is continuous at a if and only if a belongs to the domain of f and limx a [f (x) f (a)] = 0. holds true. Proof: if and only if means we must prove both directions and . Note carefully where the basic limit properties are invoked in the following steps. ( ) suppose a belongs to the domain of f and limx a [f (x) f (a)] = 0 holds true.