Warmup.

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Presentation transcript:

Warmup

Warmup

Welcome to Class A quote for today: Homework Answers: Success is the sum of small efforts, repeated day in and day out. Robert Collier (Inspirational Author) Homework Answers: Packet p. 1 & 2—“Pushed Beyond the Limit?” Answer: “There are no limits in life.”

Homework Questions?

Day 2 Limits & Continuity

Groupwork: “Exploring Continuity”

Proving Continuity In order for a function f(x) to be continuous at a point x=c the following three conditions must be met: f (c ) must exist exists, which means

Example Problem #1 Is the function continuous at x=2 ?

Example Problem #2 Is the function continuous at x=2 ?

Limits are useful for exploring continuity Example: (We will use the calculator to get the graph!) TBLSET: TblStart: 2 ∆Tbl: 0.01 The limit of a continuous function at some given value of x will be the function evaluated at that value.

Limits are useful for exploring continuity (continued) What type of discontinuity does the following function have? TBLSET: TblStart: 2 ∆Tbl: 0.01

An IMPORTANT example to explore with the calculator Tblset: Tblstart: 0 ∆tbl: 0.001 Radian Mode!!! KNOW THIS!!!