1 / 12

Evaluating Limits Analytically

Evaluating Limits Analytically. Lesson 2.3. What Is the Squeeze Theorem?. Today we look at various properties of limits, including the Squeeze Theorem. Basic Properties and Rules. Constant rule Limit of x rule Scalar multiple rule Sum rule (the limit of a sum is the sum of the limits).

dorothyv
Télécharger la présentation

Evaluating Limits Analytically

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Evaluating Limits Analytically Lesson 2.3

  2. What Is the Squeeze Theorem? Today we look at various properties of limits, including the Squeeze Theorem

  3. Basic Properties and Rules • Constant rule • Limit of x rule • Scalar multiple rule • Sum rule(the limit of a sum is the sum of the limits) See other properties pg. 79-81

  4. Limits of Functions • Limit of a polynomial P(x) • Can be demonstrated using the basic properties and rules • Similarly, note the limit of a rational function What stipulation must be made concerning D(x)?

  5. Try It Out • Evaluate the limits • Justify steps using properties

  6. General Strategies

  7. Some Examples • Consider • Why is this difficult? • Strategy: simplify the algebraic fraction

  8. Reinforce Your Conclusion • Graph the Function • Trace value close tospecified point • Use a table to evaluateclose to the point inquestion

  9. Some Examples • Rationalize the numerator of rational expression with radicals • Note possibilities for piecewise defined functions

  10. Three Special Limits • Try it out! View Graph View Graph View Graph

  11. Squeeze Rule • Given g(x) ≤ f(x) ≤ h(x) on an open interval containing cAnd … • Then

  12. Assignment • Lesson 2.3A • Page 87 • Exercises 1-43 odd • Lesson 2.3B • Page 88 • Exercises 45 – 97 EOO

More Related