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Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems
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Factoring Rational Expressions Rational Equations and Applications
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Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
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Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
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15.Functions of Several Variables
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S = contains supplemental resources
Course: Calculus II
Topic: Parametric, Polar, and Conic Curves
Subtopic: Calculus of Polar Curves

Overview

Some calculus operations can be simplified by working with equation in polar form rather than rectangular form. All the calculus we have done with rectangular equations we'll redo in this lesson but using polar form. We'll find derivatives and integrals of polar equations, slopes of tangent lines to polar curves, arc lengths of polar curves, and more.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 10.3.1 Find the derivative of a polar equation (dr/dθ)
• 10.3.2 Find the slope and equation of a tangent line to a polar curve
• 10.3.3 Find the point(s) at which the tangent line to a polar curve is horizontal or vertical
• 10.3.4 Given the graph of a polar curve identify its critical points, inflection points, relative extrema, and concavity
• 10.3.5 Set-up and evaluate the integral that gives the area under (or inside) a polar curve
• 10.3.6 Set-up and evaluate the integral that gives the area between two polar curves
• 10.3.7 Set-up and evaluate the integral that gives the arc length of a polar curve
• 10.3.8 Use integration to find the volume and surface area of a solid formed by revolving a polar curve about an axis

Supplemental Resources (optional)