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MA101: Single-Variable Calculus I

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  6. Unit 6: Applications of the Derivative
  7. 6.4: Linear Approximations
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  • 6.4: Linear Approximations

    • In this subunit, you will learn how to estimate future data points based on what you know about a previous data point and how it changed at that particular moment. This concept is extremely useful in the field of economics.

    • Whitman College: David Guichard's "Calculus, Chapter 6: Applications of the Derivative, Section 6.4: Linear Approximations" URL

      Read Section 6.4 (pages 139 and 140). In this reading, you will see how tangent lines can be used to locally approximate functions.

    • Massachusetts Institute of Technology: David Jerison's "Linear and Quadratic Approximations" Page

      Watch this video until 39:00. Beyond 39:00, Jerison discusses quadratic approximations to functions, which are in a certain sense one step beyond linear approximations. If you are interested, please continue viewing the lecture to the end.

    • Whitman College: David Guichard's "Calculus, Chapter 6: Applications of the Derivative, Exercises 6.4: Problems 1-4" URL

      Work through problems 1-4 for Exercise 6.4. When you are done, check your answers against Appendix A.

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MA101: Single-Variable Calculus I
Sections
Course Introduction
Unit 1: Analytic Geometry
Unit 2: Instantaneous Rate of Change: The Derivative
Unit 3: Rules for Finding Derivatives
Unit 4: Transcendental Functions
Unit 5: Curve Sketching
Unit 6: Applications of the Derivative
Unit 7: Integration
Unit 8: Applications of Integration
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