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5.2.1 Introduction to Limits

5.2.1 Introduction to Limits. Today you will : Develop an intuitive idea of limit Interpret limit statements written with proper notation. Today. Sketch the graph . 5-42 . Consider the graph at right when answering the questions below. .

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5.2.1 Introduction to Limits

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  1. 5.2.1 Introduction to Limits • Todayyouwill: • Develop an intuitive idea of limit • Interpretlimitstatementswrittenwithproper notation

  2. Today

  3. Sketch the graph

  4. 5-42 Consider the graph at right when answering the questions below. a. Benny starts at the point corresponding to x = 6 and moves along the graph to the left, so he’s climbing uphill. How high does Benny think he’ll get as x gets closer to 3?

  5. 5-42 Consider the graph at right when answering the questions below. b. Benny’s sister Bertha starts at the point corresponding to x = -3 and moves to the right. How high does Bertha think she’ll get as x gets closer to 3?

  6. Limits a. Suppose Bertha alsostartsat the point where x = 5, but she moves to the left. Whatisshethinking as shegetscloser to x = 2? The limitstatement for Bertha’s scenario is

  7. Limits b. Didyou notice the ‘+’ next to the 2 in part a? What do youthinkitmeans? This iscalled a one-sidedlimit. What do youthinkitwouldmean if therewere a ‘–’ signinstead?

  8. Limits c. On the graph of problem 5-42, evaluate the following limits:

  9. Complete 5-44, 5-45 and 5-46 with your partner.

  10. Partner Work

  11. Class Discussion

  12. Limits and Tables Working with one-sided limits • Today you will: • Understand the necessary conditions for a limit to exist • Practice finding limits • Predict limits from tables

  13. Today

  14. « Intermission » Check • Use the given function f(x) shown. • Benny Bug starts at the point (2,2.5) and moves along the graph to the right. What does he think his height will be at x = 3? • This is the key to limits: what does Benny think his y-coordinate will be as x approaches a certain value?

  15. « Intermission » Check b. If Bertha starts at the point (5,1) and moves to the left, what does she think her y-value will be as x approaches 3? Write limit statements for Benny and Bertha Bug as they approach x = 3 from both sides. c. Using the same function as above, complete the following limit statements:

  16. Limit Definition It is important to be able to tell when a limit exists and when it does not. What condition must be met for a limit to exist? Rephrase the definition of a limit from the Math Notes above into your notes.

  17. 5-70: Partner Work 5-70 Sketch a function f(x) whose domain is all real numbers such that

  18. As a Class 5-71 Look at the table of values shown below for some function f(x).

  19. Partner Exit Slip Please complete and turn in the exit slip before starting on your assignment.

  20. Partner Exit Slip 5-69 The graph of f(x) is shown to the right.

  21. Assignment HW 5.2.1 5-47 to 5-54 And 5-58, 5-59, 5-61, 5-62 See yu tmrrw!

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