AP Calculus AB Objectives: Determine continuity at a point, determine one-sided limits, understand the Intermediate Value Theorem.

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Presentation transcript:

AP Calculus AB Objectives: Determine continuity at a point, determine one-sided limits, understand the Intermediate Value Theorem

Removable Discontinuity (RD) If f(x) can be made continuous by appropriately defining or redefining f(c). If we can “fix” the function by filling in the hole. A general limit must exist there.

Non-Removable Discontinuity (NRD) No way to redefine f(x) to make it continuous. There is a break, jump or asymptote. The function has NO general limit at the given x-value.

x = 0 Vertical Asymptote

(1,2) x = 1 Hole: Factoring Tech

Continuous for All Real x-values (0, 1)

Continuous for All Real x-values

x = -1 and 1 Asymptotes from Factoring

x = 3 Hole from Factoring x = -3 Asymptote from Factoring

Intermediate Value Theorem Pg. 77 If f is continuous on the closed interval [a, b] and k is any number between f(a) and f(b), then there is at least one number c in [a, b] such that f(c) = k. Lesson 5 and 6

Formative Assessment – Day 1 Pg (1-6), (7-19) odd Exit Question: Join Code 13 Type decimal answer into clicker Pg. 79 #8

AP Calculus AB Objectives: Determine continuity at a point, determine one-sided limits, understand the Intermediate Value Theorem

Solve for the missing variables

Reminders

Formative Assessment – Day 2 Pg (33, 37, 39, 41, 43, 45, 47, 50, 51, 57, 59, 60) Exit Question Join Code 13 Pg. 79 #37 Type Multiple Choice Answer into Clicker Choose all that apply (A) 0(B) 1(C) Continuous(D) -1