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Continuity

Continuity. Lesson 3.2. Continuity in Context !!??. In this context, what do you think continuity means?. Intuitive Look at Continuity. A function without breaks or jumps The graph can be drawn without lifting the pencil. . Strange Functions. A jump in the graph But it is a function

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Continuity

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  1. Continuity Lesson 3.2

  2. Continuity in Context !!?? In this context, what do you think continuity means?

  3. Intuitive Look at Continuity • A function withoutbreaks orjumps • The graph can bedrawn without lifting the pencil 

  4. Strange Functions • A jump in the graph • But it is a function • The limit at 3 does not equal the value of the function at 3 • The function does not exist at x = 0

  5. Definition of Continuity at x = c • Three conditions required • f(c) is defined • exists • Which condition is violated by each of our strange functions?

  6. Continuity on Closed Interval • Given closed interval [a, b] … • f(x) continuous if • Continuous on the open interval (a, b) • Continuous from right at x = a • Continuous from left at x = b • Example

  7. Where Are They Continuous? • Polynomial Functions • Rational Functions • Root Functions • Exponential Functions • Logarithmic Functions

  8. Where Are They Continuous? • Try it out … where are these functions continuous? • Where are they discontinuous

  9. Assignment • Lesson 3.2 • Page 175 • Exercises 1 – 27 odd

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