Clicker Question 1

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# Clicker Question 1 - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Clicker Question 1' - morley

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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
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
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.
Examples
• limx   1/(x + 4) =
• limx  x + 4 =
• limx  -x + 4 =
• limx   ex =
• limx  - ex =
• limx   (2x +3)/(x – 1) =
• limx   arctan(x ) =
Clicker Question 3
• What is limx   x / (x2 +5) ?
• A. + 
• B. - 
• C. 0
• D. 1
• E. Does not exist
Clicker Question 4
• What is limx   x 2/ (x2 +5) ?
• A. + 
• B. - 
• C. 0
• D. 1
• E. Does not exist
Clicker Question 5
• What is limx  - x 3/ (x2 +5) ?
• A. + 
• B. - 
• C. 0
• D. 1
• E. Does not exist
Nonexistent Limits at Infinity?
• Is it possible for a function to have no limit (including not + nor -)?
• If so, what is an example?
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!
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?
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.