### Day 06 - One-sided Limits - 08.25.14

 Bell Ringer    ReviewFinding limits using a tableFinding limits using a graphEpsilon-Delta Limit ProofsFinding Limit PropertiesDividing Out/Rationalizing TechniquesGive an example of two functions that agree at all but one point.Limit PropertiesLessonOne-sided Limitspage 78 #1-5 (odds)page 79 #7-21 (odds)page 79 #35-51 (odds)Exit TicketFind the limit of the following function analytically.Note: Function will be written on the board in class.Create a function that has neither removable or nonremovable discontinuity. Lesson Objective(s)How are one-sided limits related to two-sided limits?How are the types of continuity similar and different?Standard(s)APC.2Define and apply the properties of limits of functions.Limits will be evaluated graphically and algebraically.Includes:​limits of a constant​limits of a sum, product, and quotient​one-sided limits​limits at infinity, infinite limits, and non-existent limits*APC.3Use limits to define continuity and determine where a function is continuous or discontinuous.Includes:​continuity in terms of limitscontinuity at a point and over a closed interval​application of the Intermediate Value Theorem and the Extreme Value Theorem​geometric understanding and interpretation of continuity and discontinuityAPC.4Investigate asymptotic and unbounded behavior in functions.Includes:describing and understanding asymptotes in terms of graphical behavior and limits involving infinity