AP Calculus Warm up
Limits at infinity
• How do you find the limit of a function when x
approaches +/- infinity?
– YOU FIND THE HORIZONTAL ASY...
How do we find the horizontal
asymptotes?
• Compare the degrees of the numerator and
denominator.
Degrees equal: It’s the ...
Rational functions
• Rational functions are fractions of 2
polynomials.
• They may have vertical or horizontal
asymptotes.
Example
1
12
lim
x
x
x
Example
13
52
lim 2
x
x
x
Example
13
52
lim 2
3
x
x
x
Practice
Evaluate each limit
xx
1
lim
13
23
lim
2
x
x
x
13
25
lim 4
4
x
xx
x
Upcoming SlideShare
Loading in …5
×

Ap calculus warm up 8.27.13

513 views

Published on

Published in: Technology, Education
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
513
On SlideShare
0
From Embeds
0
Number of Embeds
6
Actions
Shares
0
Downloads
4
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Ap calculus warm up 8.27.13

  1. 1. AP Calculus Warm up
  2. 2. Limits at infinity • How do you find the limit of a function when x approaches +/- infinity? – YOU FIND THE HORIZONTAL ASYMPTOTES Tells you the end behavior of the graph.)(lim xf x
  3. 3. How do we find the horizontal asymptotes? • Compare the degrees of the numerator and denominator. Degrees equal: It’s the ratio of the leading coefficients. Degree of numerator is greatest: No asymptote. The function is unbounded at the ends. (Goes on forever to infinity) Degree of denominator is greatest: y = 0 (x-axis) is horizontal asymptote
  4. 4. Rational functions • Rational functions are fractions of 2 polynomials. • They may have vertical or horizontal asymptotes.
  5. 5. Example 1 12 lim x x x
  6. 6. Example 13 52 lim 2 x x x
  7. 7. Example 13 52 lim 2 3 x x x
  8. 8. Practice Evaluate each limit xx 1 lim 13 23 lim 2 x x x 13 25 lim 4 4 x xx x

×