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lecture15hout - MATH 006 Calculus and Linear Algebra...

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Unformatted text preview: MATH 006 Calculus and Linear Algebra (Lecture 15) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 15 Outline 1 Infinite Limits 2 Vertical Asymptotes 3 Limits at Infinity 4 Horizontal Asymptotes Albert Ku (HKUST) MATH 006 2 / 15 Infinite Limits Infinite Limits First we consider the following examples: Example Let f ( x ) = 1 x- 1 , g ( x ) = 1 ( x- 2) 2 . Find lim x → 1 + f ( x ) lim x → 1- f ( x ) lim x → 2 + g ( x ) lim x → 2- g ( x ) By the theorem mentioned in the last lecture, all of the above limits do not exist. However, more can be said about these limits. Albert Ku (HKUST) MATH 006 3 / 15 Infinite Limits Graphs of f and g We can plot the graphs of f and g and observe the behaviour of f ( x ) when x tends to 1 and the behaviour of g ( x ) when x tends to 2. When x tends to 1 from the right, f ( x ) tends to ∞ When x tends to 1 from the left, f ( x ) tends to-∞ When x tends to 2 from the right, g ( x ) tends to ∞ When x tends to 2 from the left, g ( x ) tends to ∞ A limit that goes to ∞ or-∞ is called an infinite limit . Albert Ku (HKUST) MATH 006 4 / 15 Vertical Asymptotes Vertical Asymptotes Definition The vertical line x = a is a vertical asymptote for the graph of y = f ( x ) if f ( x ) → ∞ , or f ( x ) → -∞...
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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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lecture15hout - MATH 006 Calculus and Linear Algebra...

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