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Unformatted text preview: Outline Limits as x â†’ Â±âˆž Asymptotes Math 1205 Â§ 2.4: Limits at âˆž Â§ 2.5: Asymptotes Heath David Hart Fall 2007 Heath David Hart Math 1205 Â§ 2.4: Limits at âˆž Â§ 2.5: Asymptotes Outline Limits as x â†’ Â±âˆž Asymptotes Review Table of Contents: Notes for Day 6: Â§ 2.5: Asymptotes Review Limits as x â†’ Â±âˆž Definition Rational Function Rule Asymptotes Horizontal Asymptotes Vertical Asymptotes Oblique Asymptotes Heath David Hart Math 1205 Â§ 2.4: Limits at âˆž Â§ 2.5: Asymptotes Outline Limits as x â†’ Â±âˆž Asymptotes Review Review Last time, we discussed onesided limits in more depth, and the limit lim Î¸ â†’ sin Î¸ Î¸ = 1. Heath David Hart Math 1205 Â§ 2.4: Limits at âˆž Â§ 2.5: Asymptotes Outline Limits as x â†’ Â±âˆž Asymptotes Definition Rational Function Rule Limits as x â†’ Â±âˆž We can consider limits of the form lim x â†’âˆž f ( x ) or lim x â†’âˆž f ( x ) as special cases of onesided limits. Heath David Hart Math 1205 Â§ 2.4: Limits at âˆž Â§ 2.5: Asymptotes Outline Limits as x â†’ Â±âˆž Asymptotes Definition Rational Function Rule Limits as x â†’ Â±âˆž These limits as x approaches âˆž orâˆž correspond exactly with horizontal asymptotes of the graph of f ( x ). If for some function f ( x ), lim x â†’âˆž f ( x ) = L , then the function also has a horizontal asymptote at y = L . Heath David Hart Math 1205 Â§ 2.4: Limits at âˆž Â§ 2.5: Asymptotes Outline Limits as x â†’ Â±âˆž Asymptotes Definition Rational Function Rule Example 6a*: lim x â†’âˆž 1 x ....
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 Fall '08
 FBHinkelmann
 Calculus, Asymptotes, Limits, Limit of a function, Rational function, Heath David Hart, Rational Function Rule

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