Continuity and One-Sided Limits Day 3 - §1.4 Continuity and One-Sided Limits AP Calculus BC September 6, 2016

Entry Task Using a marker draw on the back board or window: One function that is continuous Two functions that are not continuous

Learning Targets I can apply the concepts of continuity and one-sided limits to analyze functions. I defined continuity, and determined continuity at a point and on open-and closed intervals. I correctly evaluated one-sided limits. I explained and used the Intermediate Value Theorem to analyze functions.

Review Assignment #2 Any Questions? Go over

Continuous Functions Which functions are continuous? Which functions are not continuous? What are characteristics of discontinuous functions? How can that help us define continuous functions?

Intermediate Value Theorem How do we know that f(x)=x3 – 6x2 + 5x + 12 has zero on the interval [2, 5]?

Exit Ticket Determine the continuity of this function? 𝒇 𝒙 =𝒙+𝒔𝒊𝒏(𝒙) on the interval −𝟑,𝟑 Does the following function have a 0 on the closed interval 𝟎,𝟏 𝒇 𝒙 = 𝒙 𝟑 +𝟐𝒙 −𝟏

Assignment #3 Due tomorrow Do §1.4 #8, 11, 47, 54, 55, 67, 91, 94, 115 Due by September 9 (Friday) signed syllabus page