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AP Calculus BC Wednesday, 23 October 2013

AP Calculus BC Wednesday, 23 October 2013. OBJECTIVE TSW determine limits at infinity. TESTS are graded. Sec. 3.5: Limits at Infinity. Sec. 3.5: Limits at Infinity. Sec. 3.5: Limits at Infinity. Sec. 3.5: Limits at Infinity.

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AP Calculus BC Wednesday, 23 October 2013

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  1. AP Calculus BCWednesday, 23 October 2013 • OBJECTIVE TSW determine limits at infinity. • TESTSare graded.

  2. Sec. 3.5: Limits at Infinity

  3. Sec. 3.5: Limits at Infinity

  4. Sec. 3.5: Limits at Infinity

  5. Sec. 3.5: Limits at Infinity Limits at infinity have many of the same properties of limits at specific values.

  6. Sec. 3.5: Limits at Infinity

  7. Sec. 3.5: Limits at Infinity Ex: Find each limit: Apply “Limits at Infinity” theorem. Divide numerator and denominator by the highest power of the variable.

  8. Sec. 3.5: Limits at Infinity Ex: Find each limit:

  9. Sec. 3.5: Limits at Infinity Ex: Find each limit:

  10. Sec. 3.5: Limits at Infinity How to find horizontal asymptotes: • Degree of Num. < Degree of Denom.HA:y = 0 • Degree of Num. = Degree of Denom.HA: • Degree of Num. > Degree of Denom.HA:none

  11. Sec. 3.5: Limits at Infinity Ex: Find each limit:

  12. Sec. 3.5: Limits at Infinity Ex: Find each limit:

  13. Sec. 3.5: Limits at Infinity Ex: Without a calculator, graph. Look for intercepts, extrema, inflection points, and asymptotes: Domain: R ≠ 2 x-intercept: y = 0 y-intercept: x = 0

  14. Sec. 3.5: Limits at Infinity Ex: Without a calculator, graph. Look for intercepts, extrema, inflection points, and asymptotes: Domain: R ≠ 2 Since 2 is not in the domain, there are no extrema.

  15. Sec. 3.5: Limits at Infinity Ex: Without a calculator, graph. Look for intercepts, extrema, inflection points, and asymptotes: Domain: R ≠ 2 Since 2 is not in the domain, there are no inflection points. Vertical asymptote: x = 2 Horizontal asymptote: y = 1

  16. Sec. 3.5: Limits at Infinity Ex: Without a calculator, graph. Look for intercepts, extrema, inflection points, and asymptotes: Domain: R ≠ 2 Concavity is not requested, but it will be helpful to know. + − 2 0 3  

  17. Sec. 3.5: Limits at Infinity Ex: Without a calculator, graph. Look for intercepts, extrema, inflection points, and asymptotes: Domain: R ≠ 2 x-intercept: y-intercept: No extrema, no POI Vertical asymptote: x = 2 Horizontal asymptote: y = 1 CD: (2, ∞) CU: (−∞, 2),

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