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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.

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Clicker Question 1

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  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.

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