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Calculus II (MAT 146) Dr. Day Monday Nov 18, 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.
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Calculus II (MAT 146)Dr. Day Monday Nov 18, 2013 • Series Convergence Tests: Practice and Reflect • Using Series to Re-Express Functions! • Assignments and Announcements MAT 146
Converge or Diverge? MAT 146
Converge or Diverge? MAT 146
Converge or Diverge? MAT 146
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
Power Series • The sum is a function with domain the set of all xvalues for which the series converges. • The function seems to be a polynomial, except it has an infinite number of terms. MAT 146
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
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
Power Series Convergence • For what values of x does this series converge? • Determine its Radius of Convergence and its Interval of Convergence. MAT 146
Power Series Convergence • For what values of x does this series converge? • Determine its Radius of Convergence and its Interval of Convergence. MAT 146
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
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
Power Series Convergence • For what values of x does this series converge? • Determine its Radius of Convergence and its Interval of Convergence. MAT 146
Assignments Homework Tasks • Today: Quiz #8 due! • This Week: 11.7 (Today) and 11.8 (Wed) • After Break: 11.9 (Wed 12/4) and 11.10 (Fri 12/6) • By the Day of Semester Exam: Four Review Assignments Also • Test #4: This Week Thurs and Fri (11/21 and 11/22) • Help Session Wednesday Night: STV 214, 6:15 pm – 7:30 pm • Check Your Semester Exam Schedule! • Semester Extra-Credit Option: Due December 2 MAT 146