Power Series Convergence, Calculus BC

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Power Series Convergence

Power series:
Power series can be convergence on an interval of x
Test for power series convergence:

Use ratio test to check for absolute convergence
If not absolutely convergent, solve for x value when it is absolutely convergent
Check x bounds for convergence by plugging in x to create series

Power Series Convergence

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

Intro

Power Series

Definition

Radius & Interval of Convergence

Example 1

Example 2

Example 3

Example 4

I. Prerequisites
	Parametric Curves	10:10
	Polar Coordinates	14:54
	Vector Functions	12:05
II. Differentiation
	Parametric Differentiation	13:15
	Polar Differentiation	10:14
	L'Hopital's Rule	6:43
III. Integration
	Integration By Parts	19:04
	Integration By Partial Fractions	22:04
	Improper Integrals	19:01
IV. Applications of Integration
	Logistic Growth	19:16
	Arc Length for Parametric & Polar Curves	17:40
	Area for Parametric & Polar Curves	4:33
V. Sequences, Series, & Approximations
	Definition & Convergence	7:10
	Geometric Series	10:59
	Harmonic & P Series	3:58
	Integral Test	11:31
	Comparison Test	7:47
	Limit Comparison Test	9:40
	Ratio Test	11:20
	Alternating Series	9:11
	Absolute Convergence	7:13
	Power Series Convergence	12:52
	Taylor Series	15:11
	Power Series Operations	16:40
	Lagrange Error	7:09
VI. Practice Test
	AP Calc BC Practice Test Section 1: Multi Choice Part 1	15:45
	AP Calc BC Practice Test Section 1: Multi Choice Part 2	21:38
	AP Calc BC Practice Test Section 1: Multi Choice Part 3	17:31
	AP Calc BC Practice Test Section 1: Multi Choice Part 4	14:17
	AP Calc BC Practice Test Section 1: Multi Choice Part 5	22:45
	AP Calc BC Practice Test Section 1: Free Response Part 1	9:55
	AP Calc BC Practice Test Section 1: Free Response Part 2	10:08
	AP Calc BC Practice Test Section 1: Free Response Part 3	13:58

Mathematics: AP Calculus BC

I. Prerequisites
	Parametric Curves			10:10
		Intro		0:00
		Parametric Equations		0:23
			Familiar Functions	0:32
			Parametric Equation/ Function	0:56
		Example 1: Graph Parametric Equation		1:48
		Example 2		4:30
		Example 3		6:01
		Example 4		7:12
		Example 5		8:10
	Polar Coordinates			14:54
		Intro		0:00
		Polar Coordinates		0:09
			Definition	0:11
			Example	0:23
		Converting Polar Coordinates		1:49
		Example: Convert Polar Equation to Cartesian Coordinates		3:06
		Example: Convert Polar Equation to Cartesian Coordinates		5:21
		Example: Find the Polar Representation		6:51
		Example: Find the Polar Representation		8:39
		Example: Sketch the Graph		10:02
	Vector Functions			12:05
		Intro		0:00
		Vector Functions		0:11
			2 Parts	0:18
		Example 1		1:44
		Example 2		3:52
		Example 3		4:59
		Example 4		6:03
		Example 5		8:00
		Example 6		9:23
		Example 7		10:16
II. Differentiation
	Parametric Differentiation			13:15
		Intro		0:00
		Parametric Differentiation		0:15
		Example 1		1:16
		Example 2		1:54
		Example 3		3:15
		Example 4		4:59
		Parametric Differentiation: Position, Speed & Acceleration		7:45
		Example 5		8:32
		Example 6		10:37
	Polar Differentiation			10:14
		Intro		0:00
		Polar Differentiation		0:11
			Goal	0:13
			Method	0:24
		Example 1		0:52
		Example 2		4:27
		Example 3		7:03
	L'Hopital's Rule			6:43
		Intro		0:00
		L'Hopitals Rule		0:09
			Conditions	0:14
			Limit	0:36
		Example 1		1:21
		Example 2		2:38
		Example 3		4:09
		Example 4		5:01
III. Integration
	Integration By Parts			19:04
		Intro		0:00
		Integration by Parts		0:12
			Formula	0:31
			How It's Derived From Product Rule	1:09
		Integration by Parts: Rules to Follow		3:24
			Recap of the Rules	4:13
		Example 1		4:29
		Example 2		7:04
		Example 3		8:40
		Example 4		13:48
		Example 5		15:36
	Integration By Partial Fractions			22:04
		Intro		0:00
		Integration by Partial Fractions: Goal		0:08
		Example 1		2:10
		Example 2		7:10
		Example 3		10:06
		Example 4		14:23
		Example 5		16:26
	Improper Integrals			19:01
		Intro		0:00
		Improper Integrals		0:06
			3 Steps	1:11
		Example 1		1:46
		Example 2		3:20
		Example 3		6:05
		Example 4		9:02
		Example 5		11:21
		Example 6		15:54
IV. Applications of Integration
	Logistic Growth			19:16
		Intro		0:00
		Logistic Growth Function		0:07
			Defining Variables	0:40
			Equation Parts	1:51
		Logistic Growth		2:04
		Example 1		2:59
		Example 2		7:13
		Example 3		11:29
		Example 4		15:21
	Arc Length for Parametric & Polar Curves			17:40
		Intro		0:00
		Arc Length		0:13
			Arc Length of a Normal Function	0:24
			Example	1:27
		Example 2: Arc Length for Parametric Curves		3:31
		Example 3: Arc Length for Parametric Curves		4:23
		Example 4: Arc Length for Parametric Curves		8:05
		Example 5: Arc Length for Parametric Curves		12:22
		Example 6: Arc Length for Polar Curves		15:36
		Example 7: Arc Length for Polar Curves		16:03
	Area for Parametric & Polar Curves			4:33
		Intro		0:00
		Area for Parametric Curves: Parametric Function		0:10
		Example 1: Area for Parametric Curves		0:35
		Area for Parametric Curves: Polar Function		2:50
		Example 2: Area for Polar Curves		3:18
V. Sequences, Series, & Approximations
	Definition & Convergence			7:10
		Intro		0:00
		Sequences: Definition		0:09
			Definition	0:31
			Example 1	1:07
		Sequences: Convergence		2:02
		Example 1		2:52
		Example 2		3:36
		Example 3		4:47
		Example 4		6:16
	Geometric Series			10:59
		Intro		0:00
		Geometric Series		0:07
			Definition	0:24
			Expanded Form	0:39
			Convergence Rules	1:00
		Example 1: Convergence		1:22
		Example 2: Convergence		2:36
		Example 3: Convergence		3:45
		Sum of Series		5:04
			Sum of First n Terms	5:14
			Sum of Series	5:24
		Example 1: Sum of Series		5:39
		Example 2: Sum of Series		7:15
		Example 3: Sum of Series		8:24
		Example 4: Sum of Series		9:36
	Harmonic & P Series			3:58
		Intro		0:00
		Harmonic Series		0:08
		P-Series		1:17
		Example 1: P-Series Test		2:22
		Example 2: P-Series Test		3:06
	Integral Test			11:31
		Intro		0:00
		Integral Test		0:09
		Example 1		0:54
		Example 2		4:00
		Example 3		7:59
		Example 4		9:47
	Comparison Test			7:47
		Intro		0:00
		Comparison Test		0:10
		Example 1		1:07
		Example 2		2:33
		Example 3		4:20
		Example 4		6:29
	Limit Comparison Test			9:40
		Intro		0:00
		Limit Comparison Test		0:09
			Conditions	0:31
		Example 1		1:01
		Example 2		2:53
		Example 3		4:15
		Example 4		6:19
	Ratio Test			11:20
		Intro		0:00
		Ratio Test		0:09
		Example 1		0:57
		Example 2		2:55
		Example 3		6:27
		Example 4		8:36
	Alternating Series			9:11
		Intro		0:00
		Alternating Series		0:08
		Convergence Test		0:59
		Example 1		1:27
		Example 2		2:42
		Example 3		4:57
		Example 4		6:37
	Absolute Convergence			7:13
		Intro		0:00
		Absolute Convergence		0:12
		Example 1		0:52
		Example 2		3:42
		Example 3		5:21
	Power Series Convergence			12:52
		Intro		0:00
		Power Series		0:09
			Definition	0:19
		Radius & Interval of Convergence		2:07
		Example 1		2:28
		Example 2		4:18
		Example 3		6:20
		Example 4		9:11
	Taylor Series			15:11
		Intro		0:00
		Taylor Series		0:06
			MacLaurin Series	0:45
		Example 1		1:02
		Example 2		2:45
		Example 3		6:04
		Example 4		8:23
		Example 5		11:49
	Power Series Operations			16:40
		Intro		0:00
		Operations		0:07
		Example 1: Substitution		1:05
		Example 2: Substitution		3:41
		Example 3: Differentiation/ Integration		5:39
		Example 4: Differentiation/ Integration		9:55
		Example 5: Multiplying/ Dividing		12:32
		Example 6: Multiplying/ Dividing		14:50
	Lagrange Error			7:09
		Intro		0:00
		Power Series: Lagrange Error		0:06
			Lagrange Remainder	0:21
			Lagrange Error Bound	0:50
		Example 1		1:06
		Example 2		3:27
VI. Practice Test
	AP Calc BC Practice Test Section 1: Multi Choice Part 1			15:45
		Intro		0:00
		Practice Problem 1		0:10
		Practice Problem 2		1:19
		Practice Problem 3		2:33
		Practice Problem 4		5:25
		Practice Problem 5		6:32
		Practice Problem 6		9:11
		Practice Problem 7		11:31
		Practice Problem 8		13:08
		Practice Problem 9		14:16
	AP Calc BC Practice Test Section 1: Multi Choice Part 2			21:38
		Intro		0:00
		Practice Problem 10		0:12
		Practice Problem 11		3:03
		Practice Problem 12		4:53
		Practice Problem 13		6:56
		Practice Problem 14		9:10
		Practice Problem 15		12:17
		Practice Problem 16		14:43
		Practice Problem 17		16:18
		Practice Problem 18		18:34
	AP Calc BC Practice Test Section 1: Multi Choice Part 3			17:31
		Intro		0:00
		Practice Problem 19		0:09
		Practice Problem 20		3:03
		Practice Problem 21		4:07
		Practice Problem 22		5:41
		Practice Problem 23		8:48
		Practice Problem 24		11:16
		Practice Problem 25		12:53
		Practice Problem 26		14:12
		Practice Problem 27		15:21
	AP Calc BC Practice Test Section 1: Multi Choice Part 4			14:17
		Intro		0:00
		Practice Problem 28		0:08
		Practice Problem 29		1:19
		Practice Problem 30		2:15
		Practice Problem 31		4:19
		Practice Problem 32		6:54
		Practice Problem 33		8:13
		Practice Problem 34		9:03
		Practice Problem 35		10:21
		Practice Problem 36		11:42
	AP Calc BC Practice Test Section 1: Multi Choice Part 5			22:45
		Intro		0:00
		Practice Problem 37		0:10
		Practice Problem 38		4:09
		Practice Problem 39		7:21
		Practice Problem 40		9:42
		Practice Problem 41		11:35
		Practice Problem 42		14:01
		Practice Problem 43		15:50
		Practice Problem 44		16:43
		Practice Problem 45		19:35
	AP Calc BC Practice Test Section 1: Free Response Part 1			9:55
		Intro		0:00
		Practice Problem 1a		0:08
		Practice Problem 1b		1:30
		Practice Problem 1c		3:08
		Practice Problem 2a		3:50
		Practice Problem 2b		5:40
		Practice Problem 2c		7:24
	AP Calc BC Practice Test Section 1: Free Response Part 2			10:08
		Intro		0:00
		Practice Problem 3a		0:09
		Practice Problem 3b		3:01
		Practice Problem 4a		3:55
		Practice Problem 4b		5:43
	AP Calc BC Practice Test Section 1: Free Response Part 3			13:58
		Intro		0:00
		Practice Problem 5a		0:07
		Practice Problem 5b		2:21
		Practice Problem 5c		4:21
		Practice Problem 6a		6:16
		Practice Problem 6b		8:57
		Practice Problem 6c		11:03

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Power Series Convergence

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Features Overview

Power Series Convergence

Power Series Convergence

Mathematics: AP Calculus BC

Related Books

Related Books

	Princeton Review: Cracking the AP Calculus AB & BC Exams, 2013 Authors: Princeton Review, David Kahn ISBN: 307944867 Publisher: Princeton Review Year: 2012 The book includes 5 full length practice tests with detailed explanations, and a review of all the topics tested from derivatives to integrals to logarithmic functions.
	Cliffs AP: Calculus AB & BC, 3rd Edition Authors: Dale W Johnson, Kerry J King ISBN: 764586831 Publisher: Cliffs Notes Year: 2001 The book has a topic-by topic breakdown and lots of problem approach suggestions for both free response and multiple choice calculus questions. The book also includes two full length tests.