Brief Calculus and Its Applications

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  • Edition: 11th
  • Format: Paperback
  • Copyright: 1/1/2010
  • Publisher: Prentice Hall
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Normal 0 false false false MicrosoftInternetExplorer4 This extremely readable, highly regarded, and widely adopted text presents innovative ways for applying calculus to real-world situations in the business, economics, life science, and social science disciplines. The texts' straightforward, engaging approach fosters the growth of both the student's mathematical maturity and his/her appreciation for the usefulness of mathematics. The authors' tried and true formula - pairing substantial amounts of graphical analysis and informal geometric proofs with an abundance of hands-on exercises - has proven to be tremendously successful with both students and instructors. Functions; The Derivative; Applications of the Derivative; Techniques of Differentiation; Logarithm Functions; Applications of the Exponential and Natural Logarithmic Functions; The Definite Integral; Functions of Several Variables; The Trigonometric Functions For all readers interested in applied calculus.

Table of Contents

Functions and Their Graphs
Some Important Functions
The Algebra of Functions
Zeros of Functions - The Quadratic Formula and Factoring
Exponents and Power Functions
Functions and Graphs in Applications
The Derivative
The Slope of a Straight Line
The Slope of a Curve at a Point
The Derivative
Limits and the Derivative
Differentiability and Continuity
Some Rules for Differentiation
More About Derivatives
The Derivative as a Rate of Change
Applications of the Derivative
Describing Graphs of Functions
The First and Second Derivative Rules
The First and Second Derivative Tests and Curve Sketching
Curve Sketching (Conclusion)
Optimization Problems
Further Optimization Problems
Applications of Derivatives to Business and Economics
Techniques of Differentiation
The Product and Quotient Rules
The Chain Rule and the General Power Rule
Implicit Differentiation and Related Rates
Logarithm Functions
Exponential Functions
The Exponential Function e x
Differentiation of Exponential Functions
The Natural Logarithm Function
The Derivative of lnx
Properties of the Natural Logarithm Function
Applications of the Exponential and Natural Logarithmic Functions
Exponential Growth and Decay
Compound Interest
Applications of the Natural Logarithm Function to Economics
Further Exponential Models
The Definite Integral
Areas and Riemann Sums
Definite Integrals and
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