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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.

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