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

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15 Sep 2018

School

Department

Course

Professor

Miami University

MTH 251

Calculus II

Spring 2018

Final Exam

Prof: Konstantinos Beros

Exam Guide

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

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