The document discusses infinite limits and determining vertical asymptotes from rational functions. It provides examples of limits that approach positive or negative infinity as the input increases or decreases without bound. It also gives examples of determining the vertical asymptote(s) of rational functions by finding the values that make the denominator equal to zero. Students are provided with practice problems finding vertical asymptotes of rational functions and evaluating limits that may approach positive or negative infinity.
3. Volcano: Pick an M, there is always an f(x) that is higher. Bottomless pit: Pick an N, there is always an f(x) that is lower
4. Ex 1 p.84 Determining limits from a graph FIND: Can anyone name the vertical asymptote(s) for each?
5. p. 84,85 Each of the preceding parts from Ex. 1 were rational functions, and the asymptote occurs at a number that makes the denominator 0. In general,
6. Like Ex 2 p. 85, Finding Vertical Asymptotes. Determine all vertical asymptotes: Hint: rewrite as ratio
7. Ex 3 p. 86 Rational Function with Common Factors Determine all vertical asymptotes.
8. Ex 4 p.86 Determining Infinite Limits Find each limit.
