Problem Details

Calculus: Early Transcendentals 6th Edition

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Chapter 1 Chapter 1: FUNCTIONS AND MODELS

Section 1 Section 1: Four Ways to Represent a Function

Section 2 Section 2: Mathematical Models: A Catalog of Essential Functions

Section 3 Section 3: New Functions from Old Functions

Section 4 Section 4: Graphing Calculators and Computers

Section 5 Section 5: Exponential Functions

Section 6 Section 6: Inverse Functions and Logarithms

Section 7 Section 7: Review

Chapter 2 Chapter 2: LIMITS AND DERIVATIVES

Section 1 Section 1: The Tangent and Velocity Problems

Section 2 Section 2: The Limit of a Function

Section 3 Section 3: Calculating Limits Using the Limit Laws

Section 4 Section 4: The Precise Definition of a Limit

Section 5 Section 5: Continuity

Section 6 Section 6: Limits at Infinity; Horizontal Asymptotes

Section 7 Section 7: Derivatives and Rates of Change

Section 8 Section 8: The Derivative as a Function

Chapter 3 Chapter 3: DIFFERENTIATION RULES

Section 1 Section 1: Derivatives of Polynomials and Exponential Functions

Section 2 Section 2: The Product and Quotient Rules

Section 3 Section 3: Derivatives of Trigonometric Functions

Section 4 Section 4: The Chain Rule

Section 5 Section 5: Implicit Differentiation

Section 6 Section 6: Derivatives of Logarithmic Functions

Section 7 Section 7: Rates of Change in the Natural and Social Sciences

Section 8 Section 8: Exponential Growth and Decay

Section 9 Section 9: Related Rates

Section 10 Section 10: Linear Approximations and Differentials

Section 11 Section 11: Hyperbolic Functions

Chapter 4 Chapter 4: APPLICATIONS OF DIFFERENTIATION

Section 1 Section 1: Maximum and Minimum Values

Section 2 Section 2: The Mean Value Theorem

Section 3 Section 3: How Derivatives Affect the Shape of a Graph

Section 4 Section 4: Indeterminate Forms and L'Hospital's Rule

Section 5 Section 5: Summary of Curve Sketching

Section 6 Section 6: Graphing with Calculus andCalculators

Section 7 Section 7: Optimization Problems

Section 8 Section 8: Newton's Method

Section 9 Section 9: Antiderivatives

Chapter 5 Chapter 5: INTEGRALS

Section 1 Section 1: Areas and Distances

Section 2 Section 2: The Definite Integral

Section 3 Section 3: The Fundamental Theorem of Calculus

Section 4 Section 4: Indefinite Integrals and the Net Change Theorem

Section 5 Section 5: The Substitution Rule

Chapter 6 Chapter 6: INTEGRALS

Section 1 Section 1: Areas between Curves

Section 2 Section 2: Volumes

Section 3 Section 3: Volumes by Cylindrical Shells

Section 4 Section 4: Work

Section 5 Section 5: Average Value of a Function

Chapter 7 Chapter 7: TECHNIQUES OF INTEGRATION

Section 1 Section 1: Integration by Parts

Section 2 Section 2: Trigonometric Integrals

Section 3 Section 3: Trigonometric Substitution

Section 4 Section 4: Integration of Rational Functions by Partial Fractions

Section 5 Section 5: Strategy for Integration

Section 6 Section 6: Integration Using Tables and Computer Algebra Systems

Section 7 Section 7: Approximate Integration

Section 8 Section 8: Improper Integrals

Chapter 8 Chapter 8: FURTHER APPLICATIONS OF INTEGRATION

Section 1 Section 1: Arc Length

Section 2 Section 2: Area of a Surface of Revolution

Section 3 Section 3: Applications to Physics and Engineering

Section 4 Section 4: Applications to Economics and Biology

Section 5 Section 5: Probability

Chapter 9 Chapter 9: DIFFERENTIAL EQUATIONS

Section 1 Section 1: Modeling with Differential Equations

Section 2 Section 2: Direction Fields and Euler's Method

Section 3 Section 3: Separable Equations

Section 4 Section 4: Models for Population Growth

Section 5 Section 5: Linear Equations

Section 6 Section 6: Predator-Prey Systems

Chapter 10 Chapter 10: PARAMETRIC EQUATIONS AND POLAR COORDINATES

Section 1 Section 1: Curves Defined by Parametric Equations

Section 2 Section 2: Calculus with Parametric Curves

Section 3 Section 3: Polar Coordinates

Section 4 Section 4: Areas and Lengths in Polar Coordinates

Section 5 Section 5: Conic Sections

Section 6 Section 6: Conic Sections in Polar Coordinates

Section 7 Section 7: Review

Chapter 11 Chapter 11: INFINITE SEQUENCES AND SERIES

Section 1 Section 1: Sequences

Section 2 Section 2: Series

Section 3 Section 3: The Integral Test and Estimates of Sums

Section 4 Section 4: The Comparison Tests

Section 5 Section 5: Alternating Series

Section 6 Section 6: Absolute Convergence and the Ratio and Root Tests

Section 7 Section 7: Strategy for Testing Series

Section 8 Section 8: Power Series

Section 9 Section 9: Representations of Functions as Power Series

Section 10 Section 10: Taylor and Maclaurin Series

Section 11 Section 11: Applications of Taylor Polynomials

Section 13 Section 13: Review

Chapter 12 Chapter 12: VECTORS AND THE GEOMETRY OF SPACE

Section 1 Section 1: Three-Dimensional Coordinate Systems

Section 2 Section 2: Vectors

Section 3 Section 3: The Dot Product

Section 4 Section 4: The Cross Product

Section 5 Section 5: Equations of Lines and Planes

Section 6 Section 6: Cylinders and Quadric Surfaces

Chapter 13 Chapter 13: VECTOR FUNCTIONS

Section 1 Section 1: Vector Functions and Space Curves

Section 2 Section 2: Derivatives and Integrals of Vector Functions

Section 3 Section 3: Arc Length and Curvature

Section 4 Section 4: Motion in Space: Velocity and Acceleration

Chapter 14 Chapter 14: PARTIAL DERIVATIVES

Section 1 Section 1: Functions of Several Variables

Section 2 Section 2: Limits and Continuity

Section 3 Section 3: Partial Derivatives

Section 4 Section 4: Tangent Planes and Linear Approximations

Section 5 Section 5: The Chain Rule

Section 6 Section 6: Directional Derivatives and the Gradient Vector

Section 7 Section 7: Maximum and Minimum Values

Section 8 Section 8: Lagrange Multipliers

Chapter 15 Chapter 15: MULTIPLE INTEGRALS

Section 1 Section 1: Double Integrals over Rectangles

Section 2 Section 2: Iterated Integrals

Section 3 Section 3: Double Integrals over General Regions

Section 4 Section 4: Double Integrals in Polar Coordinates

Section 5 Section 5: Applications of Double Integrals

Section 6 Section 6: Triple Integrals

Section 7 Section 7: Triple Integrals in Cylindrical Coordinates

Section 8 Section 8: Triple Integrals in Spherical Coordinates

Section 9 Section 9: Change of Variables in Multiple Integrals

Chapter 16 Chapter 16: VECTOR CALCULUS

Section 1 Section 1: Vector Fields

Section 2 Section 2: Line Integrals

Section 3 Section 3: The Fundamental Theorem for Line Integrals

Section 4 Section 4: Green's Theorem

Section 5 Section 5: Curl and Divergence

Section 6 Section 6: Parametric Surfaces and Their Areas

Section 7 Section 7: Surface Integrals

Section 8 Section 8: Stokes' Theorem

Section 9 Section 9: The Divergence Theorem

Section 10 Section 10: Summary

Chapter 17 Chapter 17: SECOND-ORDER DIFFERENTIAL EQUATIONS

Section 1 Section 1: Second-Order Linear Equations

Section 2 Section 2: Nonhomogeneous Linear Equations

Section 3 Section 3: Applications of Second-Order Differential Equations

Section 4 Section 4: Series Solutions

Section 5 Section 5: Review

Problem 1.11

Report 30 1

You put some ice cubes in aglass, fill the glass with cold
water, and then let the glass sit on atable. Describe how the
temperature of the water changes as time passes. Then sketch a
rough graph of the temperature of the water as a function of the
elapsed time.

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