1 / 16

Understanding Limits: Evaluating Existence and Properties in Calculus

In this lesson, we explore the concept of limits in calculus, focusing on how to find a limit when it exists. Understanding limits involves recognizing that they represent the value a function approaches, rather than its actual value. We'll cover properties of limits including algebraic manipulation such as addition, subtraction, multiplication, division, and power. Additionally, you'll learn about one-sided limits and how to evaluate limits algebraically, including the use of substitution, factoring, and graphing calculators like the TI-83 for visual and numerical evidence.

xander-whitaker
Télécharger la présentation

Understanding Limits: Evaluating Existence and Properties in Calculus

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. Limits Day 1

  2. Bell work Find the limit if it exists.

  3. Find the limit if it exists.

  4. The limit of a function refers to the value that the function approaches, not the actual value (if any). not 1

  5. Properties of Limits: Limits can be added, subtracted, multiplied, multiplied by a constant, divided, and raised to a power. (See your book for details.) For a limit to exist, the function must approach the same value from both sides. One-sided limits approach from either the left or right side only.

  6. does not exist because the left and right hand limits do not match! left hand limit right hand limit value of the function 2 1 1 2 3 4 At x=1:

  7. because the left and right hand limits match. left hand limit right hand limit value of the function 2 1 1 2 3 4 At x=2:

  8. because the left and right hand limits match. left hand limit right hand limit value of the function 2 1 1 2 3 4 At x=3:

  9. How do you evaluate a limit algebraically? Tutorials for the Calculus Phobe Ch 1 Lesson 3

  10. Using simple substitution: Substitution does NOT always work!

  11. Why won’t substitution work for this problem? Try factoring!

  12. Use the TI-83 to find numerical or graphical evidence that the function does or does not have a limit. If the limit does not exist, decide whether the left-hand and right-hand limits exist. Page 137 #8

  13. Use the TI-83 to find numerical or graphical evidence that the function does or does not have a limit. If the limit does not exist, decide whether the left-hand and right-hand limits exist. Page 137 #10

  14. Homework Tutorials for the Calculus PhobeLesson 3 (Ch 1) Page 137 #1-27 odd, 28

More Related