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AP Calculus AB

AP Calculus AB. Day 5 Section 1.4. c. Continuity f(x) will be continuous at x = c unless one of the following occurs:. b. does not exist. a. f( c ) does not exist. c. c. c. Removable Discontinuity A graph with a “hole” in it.

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AP Calculus AB

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  1. AP Calculus AB Day 5 Section 1.4 Perkins

  2. c. Continuity f(x) will be continuous at x = c unless one of the following occurs: b. does not exist a. f(c) does not exist c c c Removable Discontinuity A graph with a “hole” in it Non-removable Discontinuity Any other type

  3. Discuss the continuity of each. Not continuous at x = 0 (V.A.) Not continuous at x = 1 Non-removable Hole in graph at (1,2) Removable Continuous function

  4. If x < 2, the function is a parabola. (continuous) If x > 2, the function is a line. (continuous) To be continuous, the two sides must also meet when x = 2. D.S. D.S.

  5. Intermediate Value Theorem If f is continuous on [a,b] and k is any number between f(a) and f(b), then there exists a number c in [a,b] such that f(c) = k. The red graph has 1 c-value. Orange has 1 c-value. Blue has 5 c-values. Translation: If you connect two dots with a continuous function, you must hit every y-value between them at least once.

  6. AP Calculus AB Day 5 Section 1.4 Perkins

  7. c. Continuity f(x) will be continuous at x = c unless one of the following occurs: b. does not exist a. f(c) does not exist Removable Discontinuity Non-removable Discontinuity

  8. Discuss the continuity of each.

  9. Intermediate Value Theorem If f is continuous on [a,b] and k is any number between f(a) and f(b), then there exists a number c in [a,b] such that f(c) = k. The red graph has 1 c-value. Orange has 1 c-value. Blue has 5 c-values. Translation: If you connect two dots with a continuous function, you must hit every y-value between them at least once.

  10. Intermediate Value Theorem If f is continuous on [a,b] and k is any number between f(a) and f(b), then there exists a number c in [a,b] such that f(c) = k.

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