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Calculus II (MAT 146) Dr. Day Thursday Nov 14, 2013

Calculus II (MAT 146) Dr. Day Thursday Nov 14, 2013. Series Convergence Tests: Practice and Reflect Using Series to Re-Express Functions! Assignments and Announcements. Converge or Diverge?. Converge or Diverge?. Converge or Diverge?. Determine Convergence or Divergence. Power Series.

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Calculus II (MAT 146) Dr. Day Thursday Nov 14, 2013

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  1. Calculus II (MAT 146)Dr. Day Thursday Nov 14, 2013 • Series Convergence Tests: Practice and Reflect • Using Series to Re-Express Functions! • Assignments and Announcements MAT 146

  2. MAT 146

  3. MAT 146

  4. MAT 146

  5. Converge or Diverge? MAT 146

  6. Converge or Diverge? MAT 146

  7. Converge or Diverge? MAT 146

  8. Determine Convergence or Divergence MAT 146

  9. Power Series • x is a variable. • The cn’s are constants, called the coefficients. • For any fixed value of x, we can test the series for convergence. MAT 146

  10. Power Series • The sum of the series is a function with domain the set of all x values for which the series converges. • The function seems to be a polynomial, except it has an infinite number of terms. MAT 146

  11. Power Series: Example • If we let cn = 1 for all n, we get a familiar series: • This geometric series has common ratio x and we know the series converges for |x| < 1. • We also know the sum of this series: MAT 146

  12. Generalized Power Series • This is called: • a power series in (x – a), or • a power series centered at a, or • a power series about a. MAT 146

  13. Power Series Convergence • For what values of x does this series converge? • Determine its Radius of Convergence and its Interval of Convergence. MAT 146

  14. Power Series Convergence • For what values of x does this series converge? • Determine its Radius of Convergence and its Interval of Convergence. MAT 146

  15. Power Series Convergence • For what values of x does this series converge? • Use the Ratio Test to determine values of x that result in a convergent series. MAT 146

  16. Power Series Convergence • For what values of x does this series converge? • Use the Ratio Test to determine values of x that result in a convergent series. MAT 146

  17. Power Series Convergence • For what values of x does this series converge? • Determine its Radius of Convergence and its Interval of Convergence. MAT 146

  18. Assignments Homework Tasks • This Weekend: Quiz #8 (due Monday 11/18) • Next Week: 11.7 (Mon 11/18) and 11.8 (Wed 11/20) • After Break: 11.9 (Wed 12/4) and 11.10 (Fri 12/6) • By the Day of Semester Exam: Four Review Assignments Also • No Class Tomorrow 11/15 (PME-NA) • Test #4: Next Week Thurs and Fri (11/21 and 11/22) • Check Your Semester Exam Schedule! • Semester Extra-Credit Option: Due December 2 MAT 146

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