Definition of Continuity A. Continuity at a Point – A function f is continuous at a point if 1. f(c) is defined 2. exists 3. *see examples.

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Definition of Continuity A. Continuity at a Point – A function f is continuous at a point if 1. f(c) is defined 2. exists 3. *see examples

B. Continuity on an Open Interval – A function is continuous on an open interval (a, b) if it is continuous at each point on the interval.

Removable - limit does exist at every point but is not continuous Non-Removable – no limit at a point and is not continuous

Tell is the function is continuous or discontinuous. If discontinuous, what kind. A.B. C. D. y = sin x

Look for vertical asymptotes then tell the type of continuity or discontinuity. A.B. C.

PG 76 #25-53 odds

Limit from the right (positive side of graph) Limit from the left (negative side of graph)

Find the limit of as x approaches -2 from the right. Find the limit of as x approaches -2 from the left.

If andthen

A. B. C.C.

What do you do if you cannot show work algebraically to solve a one-sided limit?

PG 76 #1-21 odds