Calculus 2-4 Limits and Continuity. Continuity No breaks or interruptions in a function.

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Presentation transcript:

Calculus 2-4 Limits and Continuity

Continuity No breaks or interruptions in a function

Discontinuity Any breaks in a graph

Continuity at a Point

Removable Discontinuity We can fix the discontinuity by defining the point of discontinuity.

Jump Discontinuity If the one side limits exist but are not equal. This is considered bad because it is not an easy fix.

One-Side Continuity

Continuous at all points except at 1. Jump discontinuity at 1 Right-continuous at 1

Infinite Discontinuity If one or both side limits of a function are infinite, then the function is infinite discontinuous at that point.

Basic Laws of Continuity

Continuity of Polynomial and Rational Functions

Continuity of Some Basic Functions

Continuity of Composite Functions

Problems 2.4 #1-5, 7, 13, 17, 23, 27, odd, 57, 59