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Sec 2.5: Continuity

Sec 2.5: Continuity. Continuous Function. Intuitively, any function whose graph can be sketched over its domain in one continuous motion without lifting the pencil is an example of a continuous function. Sec 2.5: Continuity. Continuity at a Point ( interior point ). Continuity Test.

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Sec 2.5: Continuity

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  1. Sec 2.5:Continuity Continuous Function Intuitively, any function whose graph can be sketched over its domain in one continuous motion without lifting the pencil is an example of a continuous function.

  2. Sec 2.5:Continuity Continuity at a Point (interior point) Continuity Test A function f(x) is continues at a point a if Example: study the continuity at x = -1

  3. Sec 2.5:Continuity Continuity at a Point (interior point) Continuity Test A function f(x) is continues at a point a if Example: study the continuity at x = 4

  4. Sec 2.5:Continuity Continuity at a Point (interior point) Continuity Test A function f(x) is continues at a point a if Example: study the continuity at x = 2

  5. Sec 2.5:Continuity Continuity at a Point (interior point) Continuity Test A function f(x) is continues at a point a if Example: study the continuity at x = -2

  6. Sec 2.5:Continuity Cont a Continuity at a Point (end point) A function f(x) is continues at an end point a if Cont from left at a Cont from right at a

  7. Sec 2.5:Continuity Types of Discontinuities. Which conditions removable discontinuity infinite discontinuity Later: oscillating discontinuity: jump discontinuity

  8. Sec 2.5:Continuity

  9. Sec 2.5:Continuity Exam1-102

  10. Sec 2.5:Continuity

  11. Sec 2.5:Continuity Exam1-122

  12. Sec 2.5:Continuity Continuous on [a, b]

  13. Sec 2.5:Continuity Remark The inverse function of any continuous one-to-one function is also continuous.

  14. Sec 2.5:Continuity Inverse Functions and Continuity The inverse function of any continuous one-to-one function is also continuous. This result is suggested from the observation that the graph of the inverse, being the reflection of the graph of ƒ across the line y = x

  15. Sec 2.5:Continuity

  16. Sec 2.5:Continuity continuous

  17. Sec 2.5:Continuity Exam1-101

  18. Sec 2.5:Continuity Geometrically, IVT says that any horizontal line between ƒ(a) and ƒ(b) will cross the curve at least once over the interval [a, b].

  19. Sec 2.5:Continuity The Intermediate Value Theorem y0=ƒ(c) 1) ƒ(x) cont on [a,b] 2) y0 between ƒ(a) and ƒ(b) c in [a,b]

  20. Sec 2.5:Continuity One use of the Intermediate Value Theorem is in locating roots of equations as in the following example.

  21. Sec 2.5:Continuity E1 TERM-121

  22. Sec 2.5:Continuity Exam1-101

  23. Sec 2.5:Continuity

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