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# 2_5 - Section 2.5 Continuity Instructor Ms Hoa...

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Section 2.5: Continuity Instructor: Ms. Hoa Nguyen Limits and Continuity To deﬁne continuity, two things must be satisﬁed: f ( a ) is deﬁned (i.e., a is in the domain of f ). lim x a f ( x ) exists. Deﬁnition : A function f is continuous at a number a if lim x a f ( x ) = f ( a ). Hence, f is discontinuous at a if: f ( a ) is NOT deﬁned. lim x a f ( x ) does not exist. lim x a f ( x ) 6 = f ( a ). Example 2 a, b, c of Section 2.5 (textbook): Remark : f is continuous at a limit of f ( x ), as x approaches a , exists. Limit of f ( x ), as x approaches a , exists ; f is continuous at a . Continuity from one side A function f is continuous from the right at a number a if lim x a + f ( x ) = f ( a ). A function f is continuous from the left at a number a if lim x a - f ( x ) = f ( a ). Example 10 of Section 2.3 and Examples 2 d and 3 of Section 2.5 (textbook): Continuity on an interval A function f is continuous on an interval

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2_5 - Section 2.5 Continuity Instructor Ms Hoa...

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