Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 10- 1
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 10 An Introductions to Calculus: Limits, Derivatives, and Integrals
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 10.1 Limits and Motion: The Tangent Problem
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Quick Review
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide What you’ll learn about Average Velocity Instantaneous Velocity Limits Revisited The Connection to Tangent Lines The Derivative … and why The derivative allows us to analyze rates of change, which are fundamental to understanding physics, economics, engineering, and even history.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Average Velocity Average velocity is the change in position divided by the change in time.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Limits at a (Informal)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Finding the Slope of a Tangent Line
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Finding the Slope of a Tangent Line
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Average Rate of Change
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Derivative at a Point
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Derivative at a Point (easier for computing)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Finding a Derivative at a Point
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Finding a Derivative at a Point
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Derivative
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Finding the Derivative of a Function
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Finding the Derivative of a Function
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 10.2 Limits and Motion: The Area Problem
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Quick Review
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Quick Review Solutions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide What you’ll learn about Distance from a Constant Velocity Distance from a Changing Velocity Limits at Infinity The Connection to Areas The Definite Integral … and why Like the tangent line problem, the area problem has many applications in every area of science, as well as historical and economic applications.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Computing Distance Traveled A car travels at an average rate of 56 miles per hour for 3 hours and 30 minutes. How far does the car travel?
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Computing Distance Traveled A car travels at an average rate of 56 miles per hour for 3 hours and 30 minutes. How far does the car travel?
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Limits at Infinity (Informal)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Definite Integral
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 10.3 More on Limits
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Quick Review
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Quick Review Solutions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide What you’ll learn about A Little History Defining a Limit Informally Properties of Limits Limits of Continuous Functions One-Sided and Two-Sided Limits Limits Involving Infinity … and why Limits are essential concepts in the development of calculus.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Limit at a (Informal)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Finding a Limit
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Finding a Limit
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Properties of Limits
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Using the Limit Properties
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Using the Limit Properties
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide One-sided and Two-sided Limits
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Finding One-Sided Limits
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Finding One-Sided Limits
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Limits at Infinity
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 10.4 Numerical Derivatives and Integrals
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Quick Review
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Quick Review Solutions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide What you’ll learn about Derivatives on a Calculator Definite Integrals on a Calculator Computing a Derivative from Data Computing a Definite Integral from Data … and why The numerical capabilities of a graphing calculator make it easy to perform many calculations that would have been exceedingly difficult in the past.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Numerical Derivative
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Computing a Numerical Derivative
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Computing a Numerical Derivative
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Numerical Integral
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Chapter Test
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Chapter Test
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Chapter Test
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Chapter Test Solutions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Chapter Test Solutions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Chapter Test Solutions