Section 2 2 LIMITS INVOLVING INFINITY Finite Limits
- Slides: 25
Section 2. 2 LIMITS INVOLVING INFINITY
Finite Limits as x Approaches Infinity �Definition 1: The line y = b is a horizontal asymptote of the graph of a function y = f(x) if either
Horizontal Asymptotes
Example 1 �Looking for horizontal asymptotes.
Example 2 �Use graphs and tables to find (a) and (b). (c) Identify all horizontal asymptotes.
Example 3 �Use graphs and tables to find (a) and (b). (c) Identify all horizontal asymptotes.
Example 4 �Use graphs and tables to find (a) and (b). (c) Identify all horizontal asymptotes.
Infinite Limits as x Approaches a �Definition 2: The line x = a is a vertical asymptote of the graph of a function y = f(x) if either
Vertical Asymptote
Example 5 �(a) Find the vertical asymptotes of the graph of f(x). (b) Describe the behavior of f(x) to the left and right of each vertical asymptote.
Example 6 �(a) Find the vertical asymptotes of the graph of f(x). (b) Describe the behavior of f(x) to the left and right of each vertical asymptote.
TOTD �
Example 7 �(a) Find the vertical asymptotes of the graph of f(x). (b) Describe the behavior of f(x) to the left and right of each vertical asymptote.
Example 8 �(a) Find the vertical asymptotes of the graph of f(x). (b) Describe the behavior of f(x) to the left and right of each vertical asymptote.
Example 9
Example 10
TOTD �
Example 11 �Show that while f and g are quite different for numerically small values of x, they are virtually identical for |x| large.
End Behavior Models �The function is (a) a right-end behavior model for iff (b) a left-end behavior model for iff
Example 12 �(a) Find a power function end behavior model for f. (b) Identify any horizontal asymptotes.
Example 13 �(a) Find a power function end behavior model for f. (b) Identify any horizontal asymptotes.
Example 14 �Find (a) a simple basic function as a right end behavior model and (b) a simple basic function as a left end behavior model for the function.
Example 15 �Find (a) a simple basic function as a right end behavior model and (b) a simple basic function as a left end behavior model for the function.
Example 16
Example 17
- Limits involving infinity asymptotes
- Infinite limits and limits at infinity
- Limits at infinity definition
- How to find horizontal asymptotes
- Horizontal asymptote rules
- Determining infinite limits
- Limits at infinity horizontal asymptotes
- Limits at infinity (horizontal asymptotes)
- Finite subordinate clause
- Learning objectives for finite and non finite verbs
- Learning objectives for finite and non finite verbs
- How to find finite and nonfinite verbs
- Finite and non finite
- Difference rule limits
- Real limits statistics
- China limits european contacts
- Chapter 21 section 5 parliament limits the english monarchy
- Chapter 19 section 2 china limits european contacts
- Parliament limits the english monarchy chapter 5 section 5
- When do density dependent factors operate most strongly
- Limits calculator
- Hilbert's paradox of the grand hotel
- D inf h character table
- Fungsi numerator
- Sigma notation with infinity
- Numbers past infinity