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Round and round in calc. we go!

Round and round in calc. we go!. Get out your assignment. Warm up. Evaluate the limit. Section 2.4 Continuity. SWBAT Define continuity and its types. Conceptual continuity. 2.4 Continuity. This implies : f ( a ) is defined f ( x ) has a limit as x approaches a

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Round and round in calc. we go!

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  1. Round and round in calc. we go! Get out your assignment

  2. Warm up Evaluate the limit

  3. Section 2.4Continuity • SWBAT • Define continuity and its types

  4. Conceptual continuity

  5. 2.4 Continuity • This implies : • f(a) is defined • f(x) has a limit as x approaches a • This limit is actually equal tof(a) .

  6. Definition (cont’d)

  7. Types of discontinuity Removable Discontinuity: “A hole in the graph” (You can algebraically REMOVE the discontinuity)

  8. Types of discontinuity (cont’d) • Infinite discontinuity: • Where the graph approaches an asymptote • It can not be algebraically removed

  9. jump discontinuity the function “jumps” from one value to another.

  10. Example • Where are each of the following functions discontinuous, and describe the type of discontinuity

  11. One-Sided Continuity • Continuity can occur from just one side:

  12. Continuity on an Interval • So far continuity has been defined to occur (or not) one point at a time. • We can also consider continuity over an entire interval at a time: • Continuous on an Interval: it is continuous at every point on that interval.

  13. Polynomials and Rational Functions • Write the interval where this function is continuous.

  14. Types of Continuous Function • We can prove the following theorem: • This means that most of the functions encountered in calculus are continuous wherever defined.

  15. Assignment 8 • p. 126 1-31 odd • Quiz tomorrow – 2.1 through 2.4 Continuity

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