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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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Clicker question 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


Clicker question 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


Limits at infinity and global asymptotes 2 6 09

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

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

Clicker Question 3

  • What is limx   x / (x2 +5) ?

    • A. + 

    • B. - 

    • C. 0

    • D. 1

    • E. Does not exist


Clicker question 4

Clicker Question 4

  • What is limx   x 2/ (x2 +5) ?

    • A. + 

    • B. - 

    • C. 0

    • D. 1

    • E. Does not exist


Clicker question 5

Clicker Question 5

  • What is limx  - x 3/ (x2 +5) ?

    • A. + 

    • B. - 

    • C. 0

    • D. 1

    • E. Does not exist


Nonexistent limits at infinity

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

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!


Examples1

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

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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