2_2-2_5 One-Sided Limits, Limit Laws, Limits at Infinity -Hass_ppt [Compatibility Mode]

# 2_2-2_5 One-Sided Limits, Limit Laws, Limits at Infinity -Hass_ppt [Compatibility Mode]

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8/24/2009 1 Calculus I Chapter 2 Limits and Continuity 3 Ways to Evaluate a Limit o Numerically o Graphically o Analytically Example: o Consider the function o What is the domain? o What happens when x "gets close" to 1? n Numerically n Graphically 1 1 ) ( 2 - - = x x x f What does it mean for a limit to exist? (Section 2.4) o For to exist we must have: for some real number L. o That is, for the limit to exist, the limit from the left and right must both exist and be equal. ) ( lim x f c x L x f x f c x c x = = + - ) ( lim ) ( lim 3 Things That Can Cause A Limit To Not Exist o Limits from the right and left differ. o Unbounded behavior. o Oscillating behavior. n CAUTION: Just because a function oscillates does not necessarily mean that the limit does not exist. Consider x x x f sin ) ( = Evaluating Limits Analytically Section 2.2 PDF created with FinePrint pdfFactory trial version http://www.pdffactory.com

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8/24/2009 2 Limit Laws Let b and c be real numbers and let n be a positive integer. Let f
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2_2-2_5 One-Sided Limits, Limit Laws, Limits at Infinity -Hass_ppt [Compatibility Mode]

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