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lecture13hout - MATH 006 Calculus and Linear...

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MATH 006 Calculus and Linear Algebra (Lecture 13) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 13
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Outline 1 Introduction to Limits 2 Properties of Limits Albert Ku (HKUST) MATH 006 2 / 13
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Introduction to Limits Limits Example Graph the function f ( x ) = x 2 - 1 x + 1 . Then find out how f ( x ) behaves as x tends to, but not equal to - 1. Albert Ku (HKUST) MATH 006 3 / 13
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Introduction to Limits Remarks As x gets close to - 1, f ( x ) gets close to - 2. We say that the limit of f ( x ) is - 2 as x tends to - 1. Notice that f ( x ) is undefined when x = - 1. The limit of f ( x ) as x tends to - 1 is well-defined even when f ( x ) is undefined at - 1. In fact, the value of f at - 1 does not affect the limit. Albert Ku (HKUST) MATH 006 4 / 13
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Introduction to Limits Definition of the Limit of a Function Definition We write lim x c f ( x ) = L or f ( x ) L as x c if f ( x ) is close to the single real number L when x tends to, but not equal to c . Remarks
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