Mr. Rizzi - Stoney Creek High School
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  • AP Calculus BC
    • Applications of Integration (Ch. 7)
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      • Limits (Ch. 1)
      • Differentiation (Ch. 2)
      • Applications of Derivatives (Ch. 3)
      • Integration (Ch. 4)
      • Logs, Exponentials, and Other Transcendentals (Ch. 5)
      • Differential Equations (Ch. 6)
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Chapter 9
Infinite Series

Week of February 28
Monday, February 28 - 
Series and Convergence​
  • Extra Notes

Tuesday, March 1 - The Integral Test and p-Series
  • Extra Notes​

​Wednesday, March 2 - Review 
  • Watch Direct Comparison Video: https://youtu.be/oZtAgihok5s
  • 9.2 #7-19 odd, 25-35 odd, 41-49 odd
  • 9.3 #1, 3, 7, 13, 25-37 odd, 71-81 odd

Thursday, March 3 - Limit Comparison Test
  • 9.4 #3-29 odd
  • Extra Notes
​
Friday, March 4 - Alternating Series Introduction
  • Review 9.2-9.4 - Answer Key​
  • Extra Notes

Week of March 7
Monday, March 7 - Alternating Series Error Bound
  • 9.5 #27, 29, 31, 35​, 37-53 odd, 63

Tuesday, March 8 - Review
  • 9.2-9.6 Practice Packet + Answer Key

Wednesday, March 9 - The Ratio Test
  • 9.6 #13-33 odd
  • Extra Notes

Thursday, March 10 - Review
  • Review Ratio Test
  • UT Quest Due Tonight at Midnight
​
Friday, March 11 - Quiz
  • Quiz 9.2-9.6
  • Homework: Watch this video: https://www.youtube.com/watch?v=8SsC5st4LnI and the video titled 10.11: DAILY VIDEO 3 (SKILL 3.D) on AP Classroom.

Week of March 14
Monday, March 14 - Taylor Polynomials (UT #1-8)
  • Go Over Quiz
  • Taylor and Maclaurin Polynomials Investigation - In Class
  • Taylor and Maclaurin Polynomial Homework - Answer Key​

Tuesday, March 15 - Lagrange Error Bound of a Taylor Polynomial
  • Lagrange Error Bound Homework - Answer Key​
​
Wednesday, March 16 - Maclaurin Series and Manipulation Involving Substitution
  • AP Problems - Answer Key

Thursday, March 17 - Manipulation of Taylor Series Involving Integration and Differentiation
  • Taylor and Maclaurin Series Worksheet (#1-12) - Answer Key​
​
Friday, March 18 - Manipulation of Taylor Series Involving Integration and Differentiation
  • Taylor and Maclaurin Series Worksheet (#13-17) - Answer Key

Week of March 21
Monday, March 21 -  Geometric Power Series and Interval of Convergence (UT #13-19) 
  • Geometric Power Series Worksheet - Answer Key​
  • Geometric Power Series AP FRQ + Answer Key

Tuesday, March 22 - Radius and Interval of Convergence Using Ratio Test (UT #9-12)
  • ​Interval of Convergence Investigation
  • ​Interval of Convergence Worksheet - Answer Key

Wednesday, March 23 - Review
  • ​​AP Free Response Questions + Answer Key

Thursday, March 24 - Review
  • Ch. 9 AP MC Review + Answer Key
  • UT Quest Due at Midnight Tonight​

​Friday, March 25 - Test
  • Ch. 9 Test (10 MC and 2 FRQ from ALL of chapter 9​)​

AP Standards for Chapter 9
Concept of series (Section 9.2)
  • A series is defined as a sequence of partial sums, and convergence is defined in terms of the limit of the sequence of partial sums. Technology can be used to explore convergence and divergence.
Series of constants (Sections 9.2-9.6)
  • Motivating examples, including decimal expansion.
  • Geometric series with applications. (9.2)
  • The harmonic series. (9.3)
  • Terms of series as areas of rectangles and their relationship to improper integrals, including the integral test and its use in testing the convergence of p-series. (9.3)
  • Comparing series to test for convergence or divergence. (9.4)
  • Alternating series with error bound. (9.5)
  • The ratio test for convergence and divergence. (9.6)
Taylor series (Sections 9.7-9.10)
  • Taylor polynomial approximation with graphical demonstration of convergence (for example, viewing graphs of various Taylor polynomials of the sine function approximating the sine curve).
  • Lagrange error bound for Taylor polynomials.
  • Maclaurin series and the general Taylor series centered at x = a.
  • Maclaurin series for the functions sin, cos, e^x, and 1/(1-x)
  • Formal manipulation of Taylor series and shortcuts to computing Taylor series, including substitution, differentiation, antidifferentiation, and the formation of new series from known series.
  • Functions defined by power series.
  • Radius and interval of convergence of power series.
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