AP Calc BC Homework - Block E

AMC 12 (grades 11 and 12): Tuesday November 14, 2023

AMC 10 (grades 9 and 10): Tuesday November 14, 2023

Top 5 of each represent St Francis in this national competition.

AMC 12 at AoPS

1. Why study series?
2. 9.2 Series and Convergence
   1. Geometric Series
   2. Limit of nth term of a Convergent Series Th,
   3. nth term test for Divergence
3. ∆Math Lab 2-1 (9.1-9.2)

1. Proofs that the Harmonic Series Diverges:
   1. Goldmakher's Short Proof
   2. Proofs part 1
   3. Proofs 2
   4. ∆Math HW Q 2-3 (ch 9.1-9,2)
2. Slides :Geometric, nth term, Integral Test, p test (92.-9.3 pdf) (keynote)

For HW

1. Textbook Problems
2. ∂Math Lab 2-3: Integral Tests

1. Convergence Test Table 1
2. Convergence Table 2
   
3. n-term Div from former 17Calc
4. Geometric Series @17Calc
5. p-series @17Calc
6. Integral Test from former 17Calc

1. FRQ Quiz on n-th term, p-series, geometric, and Integral tests.
2. Direct Comparison Test (DCT)
3. Limit Comparison Test (LCT)
4. DCT from former@ 17Calc
5. LCT from former 17Calc

1. Convergence Test Table 1
   
2. Convergence Table 2
   
3. Convergence WS

1. Q 2-5 (9.1-9.4)
2. Intro to AST Alternating Series WS
3. AST Slides
4. AST Practice
5. AST @ 17 Calc

1. Textbook Exercises
2. ∆Math Lab: LCT/AST

In class

1. Q 2-4 redo
2. page 9-13
3. Ratio Test @ 17 Calc

1. Textbook problems
2. Lab 2-3: Ratio Test

1. Review of Convergence Tests
2. Absolute vs Conditional Convergence
3. Which Test is Best #1
4. Which Test is Best #2?
5. Flowchart 1
6. Flowchart 2
7. Flowchart 3
8. HWQ on Ratio/Root Tests
9. Ch 9 MC Practice with answers

Summary by Cal-Tech student Laura Shou

David Mao Examples of comparison Tests

Calc 13 Summary

1. Go over Test 9A
2. ∆Math Examples of Maclauren and Taylor series
3. Taylor WS 1

• Textbook Problems
• Practice Taylor Series (∆Math)

1. Examples of Taylor Series Questions (∆Math)
2. HWQ 2-12 (∆Math)
3. Taylor WS 1
4. Taylor Polynomials 2 WS.pdf
   
5. Legrange Error (Taylor Theorem)
6. Error Bounds In Power Series WS

1. Textbook Exercises
2. BC Lab: Taylor 2 @ ∆Math

• Does the Alternating series ever fail? (ppt)

• Does the Alt Series Remaider ever Fail? (video)

1. HWQ 2-13(∆Math)
2. 9.8 Power Series: Intervals of Convergence
3. 9.9 Representation of Functions by Power Series

Textbook exercises
2. BC Lab: Power Series (∆ Math)

1. Error Bounds WS ( filled in)
2. HWQ 2-15

1. p 680 from Text Book
2. Error Bound HW (1-9)
   (Here are answers to check your work)

1. Gotta No
2. Fill in version
3. Ch 9 MC Practice with answers

1. Unit 10 Progress Check: MCQ Part A, B, C (AP Classroom)
2. Please upload your work to CW 2-18

• MCQ Link
• FRQ Link