1 / 11

Clicker Question 1

Clicker Question 1. What is the lim x  0- f ( x ) for the function pictured on the board? A. 2 B. 0 C. -2 D. Does not exist. Clicker Question 2. What is the lim x  0 f ( x ) for the function pictured on the board? A. 2 B. 0 C. -2 D. Does not exist.

morley
Download Presentation

Clicker Question 1

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. Clicker Question 1 • What is the limx 0-f (x ) for the function pictured on the board? • A. 2 • B. 0 • C. -2 • D. Does not exist

  2. Clicker Question 2 • What is the limx 0f (x ) for the function pictured on the board? • A. 2 • B. 0 • C. -2 • D. Does not exist

  3. Limits at Infinity and Global Asymptotes (2/6/09) • By the “limit at infinity of a function f″ we mean what f ′s value gets near as the input x goes out the positive (+) or negative (-) horizontal axis. • We write limx   f (x ) or limx  - f (x ). • It’s possible that the answer can be a number, or be  or -, or not exist.

  4. Examples • limx   1/(x + 4) = • limx  x + 4 = • limx  -x + 4 = • limx   ex = • limx  - ex = • limx   (2x +3)/(x – 1) = • limx   arctan(x ) =

  5. Clicker Question 3 • What is limx   x / (x2 +5) ? • A. +  • B. -  • C. 0 • D. 1 • E. Does not exist

  6. Clicker Question 4 • What is limx   x 2/ (x2 +5) ? • A. +  • B. -  • C. 0 • D. 1 • E. Does not exist

  7. Clicker Question 5 • What is limx  - x 3/ (x2 +5) ? • A. +  • B. -  • C. 0 • D. 1 • E. Does not exist

  8. Nonexistent Limits at Infinity? • Is it possible for a function to have no limit (including not + nor -)? • If so, what is an example?

  9. Global Asymptotes • When limx   f (x ) is a finite number a, then the graph of f has a horizontal asymptote, the line y = a . • We can also call this a global asymptote since it describes the global (as opposed to local) behavior of f . • But global asymptotes need not be horizontal lines nor even straight lines!

  10. Examples • f (x ) = x /(x – 2) has a horizontal global asymptote. What is it? • g (x ) = x2 / (x – 2) has a diagonal global asymptote. What is it? • h (x ) = x3 / (x – 2) has a parabolic global asymptote. What is it?

  11. Assignment • Monday we will have Lab #2 on power functions, polynomial functions, rational functions, and local and global behavior. • Hand-in #1 is due at 4:45 on Tuesday. • For Wednesday, please read Section 2.6 through page 137 and do Exercises 1, 3, 9, 15, 19, 28, 31, 35, 39 and 43.

More Related