Notebook Table of content Page 1 Learning Target 1 1)1-1 A Preview of Calculus 2) 1-2 Finding limits graphically and numerically 3) 1-3 Evaluating limits analytically 4) 1-4 Continuity SectionHW AssignmentCompleted?Quiz Score 1.1 p.47: 4-6, p odd, all, all 1.3 p. 67; 37,39,47- 61,115,116,118, p. 68; 80-82, 89,90, p.79; 3-14,17-20, odd,51, 61-66

1-4 Continuity Continuous : Goes on forever with no breaks, no holes, jumps, asymptote Discontinuity : 1.Hole 2.Jump: Step Discontinuity (Piecewise function) 3.Asymptote (no bounds) Removable or non-removable discontinuity

Definition of continuity at any point: 1. f(c) exist (y- coordinate exist) Eliminates: functions w/ holes 2. The y-coordinate we are approaching Eliminates: jumps & asymptote 3. AP standard : Make sure we know the definition of continuous

Prove f(x) is continuous for all values? 1. f(0) = 0+1 = 1 2.One-side limits 3. Doesn't work: therefore the function is not continuous All polynomials are continuous (0,1)

You try: 1. f(c) exist 2. 3.

AP TEST (Free response) Find the k value such that f(x) is continuous for all value

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AP TEST (Free response) Find the k value such that f(x) is continuous for all value What does this say ?

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More examples find the value of the constant (a, b, or c) that makes the function continuous.