MTH 151 Study Guide - Final Guide: Good Luck!!, 32X, Ellipse

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Miami University
MTH 251
Calculus II
Spring 2018
Final Exam
Prof: Konstantinos Beros
Exam Guide
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CONTENTS
Exam Guide Covers the Following Topics:
Chapter 11: Infinite Sequences and Series
11.9 - Representations of Functions as Power Series
11.10 - Taylor and Maclaurin Series
11.11 - Applications of Taylor Polynomials
Chapter 10: Parametric Equations and Polar Coordinates
10.1 - Curves Defined by Parametric Equation
10.2 - Calculus with Parametric Curves
10.3 - Polar Coordinates
10.4 - Areas and Lengths in Polar Coordinates
10.5 - Conic Sections
10.6 - Conic Sections in Polar Coordinates
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Chapter 11: Infinite Sequences and Series
Section 11.9 - Representations of Functions as Power Series
Review: Power Series
Consider,

We want to represent this as a power series:







For 
 




Differentiation and Integration of Power Series
If f(x) has a power series representation
 whose domain is the set of a,
x such that the series converges, then we would like to be able to differentiate and integrate f.
The following theorem tells us how
Theorem: Term-by-term differentiation and integration of power series
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