lecture16hout

# lecture16hout - MATH 006 Calculus and Linear...

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MATH 006 Calculus and Linear Algebra (Lecture 16) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 13

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Outline 1 Continuity 2 Continuity Properties 3 Solving Inequalities using Continuity Properties Albert Ku (HKUST) MATH 006 2 / 13
Continuity Continuity Given a function f , we say that f is “continuous” if its graph y = f ( x ) is “unbroken”. More rigorously, we have the following deﬁnition: Deﬁnition A function f is continuous at x = c if 1 lim x c f ( x ) exists; 2 f ( c ) is deﬁned; 3 lim x c f ( x ) = f ( c ). A function is discontinuous at x = c if it is not continous at x = c . A function is continuous on the interval a < x < b if it is continuous at each point on the interval. Albert Ku (HKUST) MATH 006 3 / 13

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Continuity Example Suppose the ﬁgure below is the graph of the function f . Discuss the continuity of f at x = - 1 , 0 , 1 , 2 and 3. Albert Ku (HKUST) MATH 006 4 / 13
Continuity Solutions According to the graph of f , we have f is discontinuous at x = - 1 because lim x →- 1 f ( x ) = 2 6 = f ( - 1). f is continuous at x = 0 because lim x 0 f ( x ) = 1 = f (0). f

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## This note was uploaded on 12/28/2010 for the course MATH MATH006 taught by Professor Forgot during the Fall '09 term at HKUST.

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lecture16hout - MATH 006 Calculus and Linear...

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