1 / 21

More Limits

More Limits. Objective: SWBAT Evaluate one sided and two sided limits, and determine if a limit exists graphically. Do Now. For the graph of f pictured, evaluate the expressions below. Do Now. Agenda. Do Now Review Limits – How to write them and evaluate them Graphically Limits Numerically

lynne
Download Presentation

More Limits

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. More Limits Objective: SWBAT Evaluate one sided and two sided limits, and determine if a limit exists graphically

  2. Do Now • For the graph of f pictured, evaluate the expressions below

  3. Do Now

  4. Agenda • Do Now • Review Limits – How to write them and evaluate them Graphically • Limits Numerically • One Sided Limits • Non-existent limits Objective: SWBAT Evaluate one sided and two sided limits, and determine if a limit exists graphically

  5. Limits • “The limit of f(x) as x approaches (or goes to) c” • This means: What function value does the function approach as x gets closer and closer to c from both sides.

  6. Agenda • Do Now • Review Limits – How to write them and evaluate them Graphically • Limits Numerically • One Sided Limits and Non-existent limits Objective: SWBAT Evaluate one sided and two sided limits, and determine if a limit exists graphically

  7. Evaluating Limits Numerically • We can test to see what number a function is getting closer and closer to numerically. • Calculators: put the following function in for Y1 • Go to Table Set, and change the independent variable(x) to ‘ask’ and the dependent variable to ‘auto’

  8. Limits - Numerically • Let’s find out what the limit of this function is as we approach x=4. Set up this table:

  9. Similarly • Check the other side!

  10. Now you try • As a table, I’ll give you a function, and an x value to approach. • Sketch a graph of the function (including any holes or asymptotes) • Create a table with values approaching from both sides. • Evaluate the limit • Put all of it on your spot on the board after checking with me.

  11. Some limits don’t exist!!!

  12. Non-Existent Limits • If a function does not converge (get closer and closer to one value) at a particular x value, we say it’s limit does not exist • i.e.

  13. Remember:One Sided Limits • We can evaluate a limit from one direction. • This is called a one sided limit The limit of the function as x approaches c from the left The limit of the function as x approaches c from the right

  14. Example

  15. Numerically-the rules!!! • If both sides of the table get closer to that value then it is that value • If both sides of the table get larger and larger in the same direction then, the limit is positive or negative infinity • If both sides of the table get larger in different directions, then the limit does not exist.

  16. Eeeeek! What if I plug in and the universe explodes? If you plug in you get 1/0 and the universe explodes. In this case, you must solve numerically, or solve graphically. Good news! It can be done in your head. • For example, what happens to 1/x as you get closer and closer to 0, from the left. (x=-.1, -.01, -.001 etc). • What about from the right? (x=.1, .01, .001 etc) • This limit does not exist.

  17. You try, in your head

  18. Together adding limits Page 87 #2

  19. Homework • Anton problem set P. 76 #4 (quick check) P. 87 (3-5, 9,10, 12, 29-32)

More Related